Like tobyink I think a regex solution is simpler and I would add the lower case letters to your look-up hash rather than uc'ing each letter or string in turn.

use strict;
use warnings;

use 5.010;

my @lettersPerButton   = ( 3, 3, 3, 3, 3, 4, 3, 4 );
my @buttons            = map { ( $_ ) x shift @lettersPerButton } 2 ..
+ 9;
my %filterMap          = map { $_ => shift @buttons } q{A} .. q{Z};
$filterMap{ lc( $_ ) } = $filterMap{ $_ } for q{A} .. q{Z};

my @toClean = qw{
   GAV18
   gAv18
   peter
   Bill34
   };

foreach my $filterClean ( @toClean )
{
    ( my $filter = $filterClean ) =~ s{([A-Za-z])}{$filterMap{ $1 }}g;
    say qq{$filterClean --> $filter};
}
[download]

The output.

GAV18 --> 42818
gAv18 --> 42818
peter --> 73837
Bill34 --> 245534
[download]

I hope this is of interest.