According to LG, LTE Bands 2/3/4/5/7/12/25/26/41, so yes.
Besides, an associate or the manager at your TMobile store should be willing to put their SIM into your phone to see if it works, in order to gain a customer. It's the cheapest advertising that can get. (And if whatever plan you get comes with a free phone [I think the K20 is free now], take it even if you don't want it. You can sell it, or keep it as a spare.)