"for allowing" after "state laws" is incorrect.
The meaning that "the state laws allow X" is not clear. Had it been "state laws that allow X" then this option would have been correct.because it conveys "grounds of violating state laws because the ban allowed X. (which sounds ambiguous)

b) "their" is not clear
c) state laws still allow X , so past tense "allowed" is incorrect
e) being - it can be written in a concise way.
lastly
d) that refers to grounds , it (may seem ambiguous but among other options u can let it go, refers to the ban) , ban violated the state laws (which allow X) or state laws allowing X (present participle form)-- hence correct.

overall, just reject the wrong ones and narrow it down. then choose.

IMO:A

Nine months after the county banned jet skis and other water bikes from the tranquil waters of Puget Sound, a judge overturned the ban on the ground of violating state laws for allowing the use of personal watercraft on common waterways.

(A) of violating state laws for allowing
(B) of their violating state laws to allow
(C) that it violates state laws that allowed - present tense for violates suggest that it is still violating - doesnt match with overturned.
(D) that it violated state laws allowing - past tense used correctly (match with overturned)
(E) that state laws were being violated allowing

Ground that is an idiom