I haven't tried it myself, but not sure if that button would still appear if the user doesn't have object permissions on the lookup entity being referenced by that field? May be worth a try. At least it would prevent users from actually creating the new lookup object, even if the button still remained.
Unfortunately, it is not possible to remove the button in a lookup.
As a variant, you can configure access rights and limit access to the button. However, there is no possibility to limit access to individual system lookups and such a setting will be applied to all lookups.
We have also registered a problem and forwarded it to the responsible R&D team for further review.