Monstrous Gate from the Lurker at the Threshold expansion

By alboy, in Arkham Horror Second Edition

If you fail the check to close a gate with the Monstrous Gate icon a monster appears, if you evade the monster does it stay at the location or is it returned to the cup.

It stays at the location, I'd say (otherwise the specification "or the Outskirts, if this would exceed the Monster Limit" wouldn't have sense)