Not those Grovers but I had some Korean-made rear-locking tuners that broke a couple of strings very quickly. So I took the rear locking screw off that came attached to the pin that pushes against the string internally, and found that where the end of the pin had been machined to a round shape, the end was very sharp. So I sanded them all down smooth, and they were fine after that.

Some types of locking tuner are hard to dismantle. I don't know if the Grovers will simply unscrew off the top of the post, but I'd give it a go.

Sometimes you can get sharp bits of chrome plating sticking out around the post string holes (can happen on any make/type of tuner in my experience) and again its a question of smoothing off as best as you can around the holes. I normally twirl the end of a round needle file in the hole, followed by a small piece of rolled up wet and dry paper. That normally cures the problem