It's always less obnoxious to approach potentially illogical situations by giving someone the benefit of doubt. So, while you collect your 'data', also do some brainstorming on area's where the feature your adding makes a ton of sense, and might even open up new sales channels or markets.
Instead of assuming there's been some catastrophic mistake you must remedy, and instead of assuming that management puts no value on your time, try assuming that they have good reasons for it that you, especially being their for a month, might not have been fully explained. Quite often the problem is communication, not intent to waste money.
At the end, if all your effort is for seemingly insignificant return, smile and do an amazing job. Repeat until you grow weary and embattled, then leave for another job with a different set of problems.
There are always circumstances that affect decisions that you may not know of. This is one of the reasons I am always encouraging artists/developers to be knowledgeable of their project at a higher level. The more you know about what's going on in the big picture, the more of an asset you can make yourself. It's also important for sanity! The OP sounds like they are stewing daily about disagreeing with the feature -- but if there is in fact a relevant reason, some of that burnout-causing heartache could have been avoided.
Dialogue and accountability two huge keys to the management/artist relationship.