I''d suggest a completely different approach, since you're using a
regular grid.
Display the grid lines if you like, but don't fill in the boxes to
obscure the map.
When a user clicks, analyse the coordinates and calculate the grid
square the click falls in.  It's only a case of dividing and checking
remainders.
This is simple enough to do client-side, or you can transmit the
coordinates as-is for server side analysis.

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