Webhooks didn't used to work well for many builds off a single repo, but I think this changed very recently in TeamCity. Thanks for the reminder - I'll take another look this week at adding web hooks. We'd still want the poll in case of any hook failures.
At the moment, Gitlab knows nothing about our builds - and we'd want to keep it simple in that regard. If we can generically configure a hook to hit TeamCity to alert of any repo updates though, that's tractable...I need to see if that's possible now.