The the_modified_date filter allows you to modify the modified date output when used for a post inside the Loop.

It is evaluated in the the_modified_date() template tag in the wp-includes/general-template.php file. Template tags must be used inside the Loop.

the_modified_date accepts 4 arguments:

1. string $the_modified_date The date the post was modified
2. string $d The date format, if empty it defaults to the value of date_format option
3. string $before What to output before the date
4. string $after What to output after the date

Example:

The following wraps the modified date in emphasis tags on output.

View the code example on Gist.