It's been a long time since I had to deal with texas laws about firearms, but I think there is a clause about having a handgun/firearm while in commission of another crime. Yup, here's the relevant one. Then there's the plate one which is what triggers that 'other than... Class C' part of the first one, since having a fictitious plate is a Class B.

So basically, the seizure they're doing is legal, although as we all know, *cough cough*, legal ain't always right.