diff --git a/test_runner/regress/test_pageserver_restarts_under_workload.py b/test_runner/regress/test_pageserver_restarts_under_workload.py
index 28159778fe..eab8b112f0 100644
--- a/test_runner/regress/test_pageserver_restarts_under_workload.py
+++ b/test_runner/regress/test_pageserver_restarts_under_workload.py
@@ -17,6 +17,12 @@ def test_pageserver_restarts_under_worload(neon_simple_env: NeonEnv, pg_bin: PgB
     n_restarts = 10
     scale = 10
 
+    # the background task may complete the init task delay after finding an
+    # active tenant, but shutdown starts right before Tenant::gc_iteration
+    env.pageserver.allowed_errors.append(
+        r".*Gc failed, retrying in \S+: Cannot run GC iteration on inactive tenant"
+    )
+
     def run_pgbench(pg: Postgres):
         connstr = pg.connstr()
         log.info(f"Start a pgbench workload on pg {connstr}")