Even reputable stores can unknowingly have defective or counterfeit products.
There is a long supply chain that goes all the way from manufacturers and their suppliers, to distributors, wholesalers, warehousing, retailers, etc..
Lots of opportunities for shady or outright criminal activities.
And many industries are getting very good at "planned obsolenscence", finding cheaper and cheaper ways to make things, deliberately allow degrading (e.g., less rust protection for metal products), unglueable plastics, and overall profit via designed in EOL (End of Life).
As for extended warranties - very likely anything that happens will not be covered if the proverbial fine print is carefully read. Rarely worth the cost.
To be somewhat helpful continue to try to find some way to clean off or remove the greasiness. The material is likely to be degrading (as mentioned by
@kira-faye and
@dingo07). So the greasiness will return.
Another option is to (if possible) replace the ear cups. You can easily find replacement cups and/or use cloth coverings. However, many of those products are low end as well. Consider them as expendable/replaceable. Try making your own coverings - thin cloth of some sort.
Does not have to be fashionable. Just functional.