I have the same thing on my referige., but its only a single stage filter. It would be better than tap water for sure. Read on the filter cartridge and see how much and what it filters, that would be a big help.
todd
Look into buying a RO/DI unit... especially being on well water. Although well water can be better than city water, it can also be worse... just depends. A RO/DI filter will provide you with pure water eliminating potential problems in the future.