As has already been stated, Text::CSV is the most robust solutionf or this type or problem:

use Text::CSV;

use strict;
use warnings;

my $inputstring = qq{field1\tfield2\t\"field3\t\t\"\tfield4\n};

my $csv = Text::CSV->new({eol => "\n", sep_char => "\t", binary => 1})
+;

$csv->parse($inputstring)
    or die "csv error: " . $csv->error_input();
my @columns = $csv->fields();

s/\t//g for (@columns);

$csv->combine(@columns)
    or die "csv error: " . $csv->error_input();
my $string = $csv->string();

print $string;
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Here's the regex solution though using double quotes that allow escaped quotes

my $inputstring = qq{field1\tfield2\t\"field3\t\t\"\tfield4\n};

$inputstring =~ s{("(?: (?> [^\"\\]+ ) | \\ . )*")}{ (my $str = $1) =~
+ s/\t//g; $str }xesg;

print $inputstring;
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