Make sure to use mint extract, not peppermint extract.
Zested limes need not go to waste. You could improvise a glaze using the juice of the limes and a small amount of rum. Mix this by the teaspoonful into a rough cup of confectioner's sugar until your desired consistency is achieved. I usually aim for slightly lighter than maple syrup in thickness. The result can be drizzled onto the still-warm cookies and allowed to dry as the cookie cools.
The step involving leaving the batter in the fridge to infuse the flavors is completely optional.