Replacing Tile Installed Over Hardibacker

I'm in the process of installing tile over most of the downstairs floors of my house. In the kitchen, with a plywood subfloor, I have installed the 13" X 13" tiles over 1/4" Hardibacker.
I did a poor job installing one of the tiles (ended up with a corner kicker) and had to remove it. In the removal process some of the Hardibacker delaminated and came up with the tile. As a result, the Hardibacker in part of the area (about half) where the replacement tile will go is between 1/16" to 1/8" lower than it should be, as a result of the delamination and pull-out.
Any advice on leveling the Hardibacker prior to installing the replacement tile? Just set it in a thicker than normal layer of thinset? Level with concrete patcher prior to installation? Cut out the square of Hardibacker and screw down a replacement piece? Other?
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I would just use a little extra thinset.
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