Can you please share more photos of the growth you're asking about? We can't see the foliage clearly enough...in some cases they do not appear to be crapemyrtle foliage, and in one area, it looks like Mile-a-Minute, an invasive and very common annual vine that should be removed (carefully, as the stems have sharp prickles). Another area looks almost like Rhododendron foliage, which would be odd, so we need a clearer and closer look.

Crapemyrtle trees often produce suckers, which are new stems arising from the trunk base or roots, and they also can produce new stems along the trunk as well, since that's their natural growth habit. You can trim off any young shoots you don't want to mature at any time, although the younger you can remove them, the better. Do not cut any stems arising from the trunk bark flush with the trunk, which could create  wound that will not seal-over well; instead, leave a very small stub (perhaps a quarter-inch), which will become less visible over time as the trunk grows larger with age.

Miri