I had what I will loosely call a builders' grade counter top. Actually, it was fiberboard with a thin laminate glued over it and up the drywall to form a splash guard.

When this was removed for cabinet replacement, the splash guard came up unevenly. In some ares, there is still a dry glue layer, other areas there is drywall paper, others are down to the drywall, and in a few areas the drywall is pitted.

What would be the best way to prep the wall for paint or tile?

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Never buy a house built by an oil company...