$1 is undefined, and any use of undef will trigger the warning. You can use the following regex if you don't want to turn the warnings off:

s{^(?:aa(bb))?.*}{defined($1)?$1:q{}}ei;
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The e switch lets you use code for the replacement, so you can test whether $1 is defined before using it, and if it's not defined, use the empty string instead.