Well, in that case the antenna I ran the analyzer on is the same one. So your GMRS radio is probably seeing something around 3:1 SWR when transmitting. Most current ham gear folds way back to save the finals in that case, not sure about a GMRS radio, although I would suspect the same.
I don't think you can actually tune these antennas, other than cutting elements - and I'm not sure that would be too easy. This antenna is three 5/8-wave stacked so you'd have to trim each of the 5/8 sections to the right length, probably by cutting and resoldering the elements - the joints probably aren't in the right places. (And it would no longer work well on ham bands, 2M or 440.)
Your best bet would be to get a separate commercial-band base antenna for GMRS. You could by one from a variety of vendors, but if you are up to building, there are plans out there for all kinds of amateur band antennas. You would just need to recalculate the lengths for the higher frequency. Then you would have an antenna tuned specifically for the frequencies of interest. (My first inclination would be a J-pole, as I've had lots of practice making those out of 1/2" copper pipe and they hold up well outdoors.)