As far as I searched, I did not find any authentic matter concerning this issue. Therefore, logically and also as a rule it could be termed Bid’ah. As a result we cannot term it Makruh, then it could be named Haram (forbidden), Since as far as I know, all sects of Islam believe that Bidah is considered as a Haram practice.
Let’s see what precisely Bid’ah is.
Bid’ah or (البدعه) literally is related to the innovation and actually, something new, and in Islamic terms, means to relate something to religion which it has in no way asserted and likewise in no way complies with any of its guidelines and sayings.
In accordance with this description, many of the Muslims’ practices aren’t considered bid’ah, given that they don’t relate what they are doing to religion, or even what those Muslims do doesn’t go under one of the general categories which is related to the religion.
Eventually wiping the neck in wudu could be termed Bid’ah. Of course you ought to pay attention that in a case you cannot term it Bid’ah(or even Makruh), and that is when you do it solely with the intention of cleaning. Actually you must be aware that is it not considered as an Islamic act and solely you do it as you like do it.