diff --git a/parsl/dataflow/dflow.py b/parsl/dataflow/dflow.py
index cc3731fae0..6cec168b5d 100644
--- a/parsl/dataflow/dflow.py
+++ b/parsl/dataflow/dflow.py
@@ -752,13 +752,6 @@ def launch_task(self, task_record: TaskRecord) -> Future:
                                                        monitor_resources=executor.monitor_resources(),
                                                        run_dir=self.run_dir)
 
-            # hint executors that this function will be monitored
-            if task_record['resource_specification']:
-                task_record['resource_specification'].update({'_is_monitoring_enabled': True})
-        else:
-            if task_record['resource_specification']:
-                task_record['resource_specification'].update({'_is_monitoring_enabled': False})
-
         with self.submitter_lock:
             exec_fu = executor.submit(function, task_record['resource_specification'], *args, **kwargs)
         self.update_task_state(task_record, States.launched)
diff --git a/parsl/executors/taskvine/executor.py b/parsl/executors/taskvine/executor.py
index 572729a6c8..d7a7bfe2ad 100644
--- a/parsl/executors/taskvine/executor.py
+++ b/parsl/executors/taskvine/executor.py
@@ -341,11 +341,15 @@ def submit(self, func, resource_specification, *args, **kwargs):
 
         logger.debug(f'Got resource specification: {resource_specification}')
 
-        is_monitoring_enabled = resource_specification.get('_is_monitoring_enabled', False)
+        # If `_parsl_monitoring_task_id` is in kwargs, Parsl monitoring code is enabled.
+        is_monitoring_enabled = '_parsl_monitoring_task_id' in kwargs
 
         # Default execution mode of apps is regular
         exec_mode = resource_specification.get('exec_mode', self.function_exec_mode)
 
+        # Fall back to regular execution if a function is Parsl-monitored as a monitored function is invocation-specific.
+        # Note that it is possible to get the wrapped function by calling the `__wrapped__` attribute when monitoring is enabled.
+        # It will disable the monitoring wrapper code however.
         if exec_mode == 'serverless' and is_monitoring_enabled:
             logger.warning("A serverless task cannot run with Parsl monitoring enabled. Falling back to execute this task as a regular task.")
             exec_mode = 'regular'