Long term consequences? Yes. The thinset mortar and the backerboard will release alkali when exposed to moisture and over time that will deteriorate the fiberglass resins in the tape. Major consequence? Meh... the tape is there to reinforce the corners and edges against minor shifting in the house structure so that it doesn't result in straining the mortar, ...
Depending on your grout gap, an oscillating tool with a grout blade could work well.
If your gaps are substantially wider, a narrow chisel might do the job.
I'd avoid any rotating tool as you're likely to slip and damage your tile.