Remove tabs only between quotation marks

[bestresearch2]

I am reading in a tab delimited text file exported from Excel. Some fields have begin and end with quotation marks because the fields themselves have non-printable characters including tabs. How do I do search/replace for just the tabs inside of strings bounded by quotation marks?

In the following example, I'd like to remove the two tabs next to field3:

$inputstring="field1\tfield2\t\"field3\t\t\"\tfield4\n";