diff --git a/contrib/postgres_fdw/deparse.c b/contrib/postgres_fdw/deparse.c
index d272719ff4..e7b3cf35ec 100644
--- a/contrib/postgres_fdw/deparse.c
+++ b/contrib/postgres_fdw/deparse.c
@@ -840,6 +840,55 @@ foreign_expr_walker(Node *node,
 	return true;
 }
 
+/*
+ * Returns true if given expr is something we'd have to send the value of
+ * to the foreign server.
+ *
+ * This should return true when the expression is a shippable node that
+ * deparseExpr would add to context->params_list.  Note that we don't care
+ * if the expression *contains* such a node, only whether one appears at top
+ * level.  We need this to detect cases where setrefs.c would recognize a
+ * false match between an fdw_exprs item (which came from the params_list)
+ * and an entry in fdw_scan_tlist (which we're considering putting the given
+ * expression into).
+ */
+bool
+is_foreign_param(PlannerInfo *root,
+				 RelOptInfo *baserel,
+				 Expr *expr)
+{
+	if (expr == NULL)
+		return false;
+
+	switch (nodeTag(expr))
+	{
+		case T_Var:
+			{
+				/* It would have to be sent unless it's a foreign Var */
+				Var		   *var = (Var *) expr;
+				PgFdwRelationInfo *fpinfo = (PgFdwRelationInfo *) (baserel->fdw_private);
+				Relids		relids;
+
+				if (IS_UPPER_REL(baserel))
+					relids = fpinfo->outerrel->relids;
+				else
+					relids = baserel->relids;
+
+				if (bms_is_member(var->varno, relids) && var->varlevelsup == 0)
+					return false;	/* foreign Var, so not a param */
+				else
+					return true;	/* it'd have to be a param */
+				break;
+			}
+		case T_Param:
+			/* Params always have to be sent to the foreign server */
+			return true;
+		default:
+			break;
+	}
+	return false;
+}
+
 /*
  * Convert type OID + typmod info into a type name we can ship to the remote
  * server.  Someplace else had better have verified that this type name is
diff --git a/contrib/postgres_fdw/expected/postgres_fdw.out b/contrib/postgres_fdw/expected/postgres_fdw.out
index c3e4c6849e..f19f982e0a 100644
--- a/contrib/postgres_fdw/expected/postgres_fdw.out
+++ b/contrib/postgres_fdw/expected/postgres_fdw.out
@@ -2827,6 +2827,46 @@ select sum(c1) from ft1 group by c2 having avg(c1 * (random() <= 1)::int) > 100
                Remote SQL: SELECT "C 1", c2 FROM "S 1"."T 1"
 (10 rows)
 
+-- Remote aggregate in combination with a local Param (for the output
+-- of an initplan) can be trouble, per bug #15781
+explain (verbose, costs off)
+select exists(select 1 from pg_enum), sum(c1) from ft1;
+                    QUERY PLAN                    
+--------------------------------------------------
+ Foreign Scan
+   Output: $0, (sum(ft1.c1))
+   Relations: Aggregate on (public.ft1)
+   Remote SQL: SELECT sum("C 1") FROM "S 1"."T 1"
+   InitPlan 1 (returns $0)
+     ->  Seq Scan on pg_catalog.pg_enum
+(6 rows)
+
+select exists(select 1 from pg_enum), sum(c1) from ft1;
+ exists |  sum   
+--------+--------
+ t      | 500500
+(1 row)
+
+explain (verbose, costs off)
+select exists(select 1 from pg_enum), sum(c1) from ft1 group by 1;
+                    QUERY PLAN                     
+---------------------------------------------------
+ GroupAggregate
+   Output: ($0), sum(ft1.c1)
+   Group Key: $0
+   InitPlan 1 (returns $0)
+     ->  Seq Scan on pg_catalog.pg_enum
+   ->  Foreign Scan on public.ft1
+         Output: $0, ft1.c1
+         Remote SQL: SELECT "C 1" FROM "S 1"."T 1"
+(8 rows)
+
+select exists(select 1 from pg_enum), sum(c1) from ft1 group by 1;
+ exists |  sum   
+--------+--------
+ t      | 500500
+(1 row)
+
 -- Testing ORDER BY, DISTINCT, FILTER, Ordered-sets and VARIADIC within aggregates
 -- ORDER BY within aggregate, same column used to order
 explain (verbose, costs off)
diff --git a/contrib/postgres_fdw/postgres_fdw.c b/contrib/postgres_fdw/postgres_fdw.c
index bfa9a1823b..27d2b0a2dd 100644
--- a/contrib/postgres_fdw/postgres_fdw.c
+++ b/contrib/postgres_fdw/postgres_fdw.c
@@ -5291,7 +5291,6 @@ foreign_grouping_ok(PlannerInfo *root, RelOptInfo *grouped_rel,
 	PgFdwRelationInfo *fpinfo = (PgFdwRelationInfo *) grouped_rel->fdw_private;
 	PathTarget *grouping_target = grouped_rel->reltarget;
 	PgFdwRelationInfo *ofpinfo;
-	List	   *aggvars;
 	ListCell   *lc;
 	int			i;
 	List	   *tlist = NIL;
@@ -5317,6 +5316,15 @@ foreign_grouping_ok(PlannerInfo *root, RelOptInfo *grouped_rel,
 	 * server.  All GROUP BY expressions will be part of the grouping target
 	 * and thus there is no need to search for them separately.  Add grouping
 	 * expressions into target list which will be passed to foreign server.
+	 *
+	 * A tricky fine point is that we must not put any expression into the
+	 * target list that is just a foreign param (that is, something that
+	 * deparse.c would conclude has to be sent to the foreign server).  If we
+	 * do, the expression will also appear in the fdw_exprs list of the plan
+	 * node, and setrefs.c will get confused and decide that the fdw_exprs
+	 * entry is actually a reference to the fdw_scan_tlist entry, resulting in
+	 * a broken plan.  Somewhat oddly, it's OK if the expression contains such
+	 * a node, as long as it's not at top level; then no match is possible.
 	 */
 	i = 0;
 	foreach(lc, grouping_target->exprs)
@@ -5337,6 +5345,13 @@ foreign_grouping_ok(PlannerInfo *root, RelOptInfo *grouped_rel,
 			if (!is_foreign_expr(root, grouped_rel, expr))
 				return false;
 
+			/*
+			 * If it would be a foreign param, we can't put it into the tlist,
+			 * so we have to fail.
+			 */
+			if (is_foreign_param(root, grouped_rel, expr))
+				return false;
+
 			/*
 			 * Pushable, so add to tlist.  We need to create a TLE for this
 			 * expression and apply the sortgroupref to it.  We cannot use
@@ -5352,9 +5367,11 @@ foreign_grouping_ok(PlannerInfo *root, RelOptInfo *grouped_rel,
 		else
 		{
 			/*
-			 * Non-grouping expression we need to compute.  Is it shippable?
+			 * Non-grouping expression we need to compute.  Can we ship it
+			 * as-is to the foreign server?
 			 */
-			if (is_foreign_expr(root, grouped_rel, expr))
+			if (is_foreign_expr(root, grouped_rel, expr) &&
+				!is_foreign_param(root, grouped_rel, expr))
 			{
 				/* Yes, so add to tlist as-is; OK to suppress duplicates */
 				tlist = add_to_flat_tlist(tlist, list_make1(expr));
@@ -5362,12 +5379,16 @@ foreign_grouping_ok(PlannerInfo *root, RelOptInfo *grouped_rel,
 			else
 			{
 				/* Not pushable as a whole; extract its Vars and aggregates */
+				List	   *aggvars;
+
 				aggvars = pull_var_clause((Node *) expr,
 										  PVC_INCLUDE_AGGREGATES);
 
 				/*
 				 * If any aggregate expression is not shippable, then we
-				 * cannot push down aggregation to the foreign server.
+				 * cannot push down aggregation to the foreign server.  (We
+				 * don't have to check is_foreign_param, since that certainly
+				 * won't return true for any such expression.)
 				 */
 				if (!is_foreign_expr(root, grouped_rel, (Expr *) aggvars))
 					return false;
@@ -5454,7 +5475,8 @@ foreign_grouping_ok(PlannerInfo *root, RelOptInfo *grouped_rel,
 			 * If aggregates within local conditions are not safe to push
 			 * down, then we cannot push down the query.  Vars are already
 			 * part of GROUP BY clause which are checked above, so no need to
-			 * access them again here.
+			 * access them again here.  Again, we need not check
+			 * is_foreign_param for a foreign aggregate.
 			 */
 			if (IsA(expr, Aggref))
 			{
diff --git a/contrib/postgres_fdw/postgres_fdw.h b/contrib/postgres_fdw/postgres_fdw.h
index a5d4011e8d..6d06421a16 100644
--- a/contrib/postgres_fdw/postgres_fdw.h
+++ b/contrib/postgres_fdw/postgres_fdw.h
@@ -140,6 +140,9 @@ extern void classifyConditions(PlannerInfo *root,
 extern bool is_foreign_expr(PlannerInfo *root,
 				RelOptInfo *baserel,
 				Expr *expr);
+extern bool is_foreign_param(PlannerInfo *root,
+				 RelOptInfo *baserel,
+				 Expr *expr);
 extern void deparseInsertSql(StringInfo buf, RangeTblEntry *rte,
 				 Index rtindex, Relation rel,
 				 List *targetAttrs, bool doNothing, List *returningList,
diff --git a/contrib/postgres_fdw/sql/postgres_fdw.sql b/contrib/postgres_fdw/sql/postgres_fdw.sql
index 613228fba8..934b6ffaf2 100644
--- a/contrib/postgres_fdw/sql/postgres_fdw.sql
+++ b/contrib/postgres_fdw/sql/postgres_fdw.sql
@@ -674,6 +674,16 @@ select count(*) from (select c5, count(c1) from ft1 group by c5, sqrt(c2) having
 explain (verbose, costs off)
 select sum(c1) from ft1 group by c2 having avg(c1 * (random() <= 1)::int) > 100 order by 1;
 
+-- Remote aggregate in combination with a local Param (for the output
+-- of an initplan) can be trouble, per bug #15781
+explain (verbose, costs off)
+select exists(select 1 from pg_enum), sum(c1) from ft1;
+select exists(select 1 from pg_enum), sum(c1) from ft1;
+
+explain (verbose, costs off)
+select exists(select 1 from pg_enum), sum(c1) from ft1 group by 1;
+select exists(select 1 from pg_enum), sum(c1) from ft1 group by 1;
+
 
 -- Testing ORDER BY, DISTINCT, FILTER, Ordered-sets and VARIADIC within aggregates