You can get your answer more quickly by firing up the debugger and just trying it out:

% perl -de 1
  DB<1> $s = 'Hello.1.txt'
  DB<2> $s =~ s/\.(?=txt$)//g   # in this case the /g is superfluous
  DB<3> p $s
Hello.1txt
[download]

And faster still (in the long run) if you just study perlre.