This ‘X’ button is part of the system control strip which MacOS Requires you to have if BTT shows the control strip. It’s just the way it’s implemented.
You can try unchecking “Show MacOS Control Strip” in “General TouchBar Settings” to remove this button, but unfortunately you will loose the control strip. (you might want to make a toggle BTT touchbar button)
I’ve achieved a way to remove the X and preserve the control strip in my preset, but currently BTT is not importing it correctly so i guess I can’t share it just yet... (sad)
Basically it’s BTT using full bar mode while an exact remake of the macOS control strip appears. So when the BTT preset is activated there is no X and the control strip remains.
See the preset here:
(currently working to fix the new version which is more relevant to you though, as i’ve only implemented the ‘no X control strip’ in version 2.)
[images coming in an edit]