Thanks Phil for your reply!
I usually remove this meta information this way:
The old 6th-10th bits were
41 64 6F 62 65 (Adobe)
and using a HEX editor I replaced them to
00 00 00 00 00 (zeros)
That's it! the meta information is removed

(that's all I wanted).
And good news is, it does not reduce the picture quality.
But the bad news is, I have to do it manually for all the files

So, instead of deleting those bits, can ExifTool not replace them to
00 (zeros)