Sneakylong If I were her I'd try that or an arm lock putter. She sucks from short range. She's ok from intermediate range.
As was shown yesterday, with the bad miss from short range on 14 followed by a very nice 15-footer from the fringe for birdie at 15.
I'm surprised that someone at Tour level who is struggling to make short putts hasn't tried carrying two putters in their bag - one for longer putts, one for short - with the 'short range' putter set up to maximise the ability to start the ball on line no matter the situation. (That might be arm lock, big grip, heavy head, different head style - whatever it takes to give the player confidence that they'll hit a solid putt on line.)
For what it's worth, I'd advise Thompson to keep it very simple - pare down the routine on short putts to: find the line, pick a small target, set up, hit the putt. Taking extra time to get it right just means more time to think about missing it (particularly when you have a history of missing short ones).