With a negative lookahead, yes: 
$string =~ s/<tr(?:(?!<tr>).)+?NOTWANTED.+?<\/tr>//gsm;

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For each char after the opening <tr, it makes sure that it's not the beginning of a closingnested tag.
Caution: Contents may have been coded under pressure.

In reply to Re: greedy/nongreedy regex replacement by Roy Johnson
in thread greedy/nongreedy regex replacement by svenXY

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