It's Gilt, service is not their strong point. That being said, it can't hurt to email.
No, call them instead. I feel this goes for pretty much any store/webstore/retailer... it always seems like whenever you email a store it takes them forever to take care of things, and for some stores nothing will happen at all. Also fwiw gilt's customer service via phone is actually pretty good, in all my dealings they've been pretty organized and quick to act.
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