Firstly, I agree with others that it would be preferable to deal with the problem at the source, rather than fixing it within your code. It's entirely possible that you'll need to repeat exactly the same fix in multiple scripts, modules or subroutines.

If that's not possible, it may be insufficient to just add a ^ anchor and remove the g option. What about hidden files (e.g. .bashrc) or places where intentionally specifying the current directory is necessary. You may need something closer to

s{^[.](?=/root(?:/|$))}{}
[download]

Consider this SSCCE:

#!/usr/bin/env perl

use strict;
use warnings;

use Test::More;

my @tests = (
    [qw{./root /root}],
    [qw{./root/ /root/}],
    [qw{./root/xyz /root/xyz}],
    [qw{./root_plus ./root_plus}],
    [qw{./not_root/ ./not_root/}],
    [qw{./script_not_in_path.pl ./script_not_in_path.pl}],
    [qw{.hidden .hidden}],
);

plan tests => 0+@tests;

for my $test (@tests) {
    my $file = $test->[0];
    $file =~ s{^[.](?=/root(?:/|$))}{};
    is $file, $test->[1];
}
[download]

Output:

1..7
ok 1
ok 2
ok 3
ok 4
ok 5
ok 6
ok 7
[download]

That's just an example. Modify the test cases to better reflect your real data.