Perl 5+-MList::Util+(min), 44 bytes

sub{$g=pop;map{min map$g=~s/$_/$_/g,/./g}@_}

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Explanation

Not entirely dissimilar to other solutions, this is a function submission in Perl (unusual I know, but 1 byte shorter than my best "standard" attempt.

Takes the last argument as a string containing the grid, and every other argument as words to find. Iterates over each word (implicitly stored in $_, splits (/./g) and maps over each letter, returning the number of s///ubstitutions replacing the letter for itself, taking the minimum for each word.