To my knowledge, there isn’t a great way to accomplish this. I’ve never had to repair a Moto X. However, As someone who deals with this issue on a weekly basis, here’s what I recommend.
Make sure the grill is a straight as possible, use a pair of tweezers to gently position the grill over it’s position. If possible, use the point of your tweezers to pinch the edges of the grill in between the speaker and phone housing. A nylon spudger is also an option if you have enough clearance, and I have been known to use a razor blade from time to time, but I have ruined more grills than I have saved with that tool. In many cases, it is advisable to dab a tiny bit of adhesive on each end to get it to stick. If you go the adhesive rout be sure to use something that isn’t too viscous but dries clear and quick. I hope this helps.
-CW