How to only get RecordingID from MusicBrainz?

If you don't want to to deselect the options in the GUI like this:


then you have to modify the used Websource Script.
Create a copy from the original file, open this copy in a texteditor and write every unwanted tag like this
set ARTIST
set TITLE
set ALBUM
...
at the end of the Websource Script. Then use/call this modified script from Mp3tag.

BTW:
There is no MusicBrainz-Tag called "RecordingID" AFAIK
MusicBrainz knows
MUSICBRAINZ_TRACKID
or
MUSICBRAINZ_RELEASETRACKID

Please see also this: