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for (@links1) {
  s/<\s*a\s.*?\b(href\s*=\s*".*?").*?>/<a $1>/i;
}

@links1=~   # that would work like scalar(@array)=~
s/ .*       # replace complete string with
...
   .*?      # as few as possible (=no) anythings
   \"       # no need to escape '"'
 /isx;      # 's' is not needed, I added 'x'