I'd change the regex to exclude quotes, rather than match everything: m,"?(/[^"]*)"?,

Test script (including some lines where I tried to break the match):

#!/usr/bin/perl
use strict;
use warnings;

while (my $line = <DATA>) {
    chomp $line;
    
    if ($line =~ m,"?(/[^"]*)"?,) {
        print "Line matched: $line ($1)\n";
    }
    else {
        print "Line didn't match: $line\n";
    }
}


__DATA__
"/moreIters 10"
"/bootMe any text here"
/fewIter
/some stuff here
"/albatross" foo bar baz
monkeys
leprechauns /not monkeys
/gnomes "not leprechauns though"
[download]

Output:

Line matched: "/moreIters 10" (/moreIters 10)
Line matched: "/bootMe any text here" (/bootMe any text here)
Line matched: /fewIter (/fewIter)
Line matched: /some stuff here (/some stuff here)
Line matched: "/albatross" foo bar baz (/albatross)
Line didn't match: monkeys
Line matched: leprechauns /not monkeys (/not monkeys)
Line matched: /gnomes "not leprechauns though" (/gnomes )
[download]