How to change header WITHOUT change of modification date?

Occasionally I want to change a MP3 header field (e.g. Title or Genre) without changing the modification date.

How can I achieve this in MP3tag?

Is there an option "no modif. date change on header change"?

Yes, see the help:
http://help.mp3tag.de/options_tags.html

Preserve timestamps of modified files

Mp3tag will keep the modification date of the files, when writing or removing tags.