How can I remove water tubing in my kitchenaide KSRS25IL SS03?

I've replaced our filters in the fridge with the standard and the very best filters for our model but we still have what can only be described as a clear strands of "something" coming out when we get the water from the fridge. The appearance of these things are like clear little scarfs but when you remove one from the water they are greasy and snoty looking. Our local municipality dept. has told me that there is some chemical in water and the way the water is filtered in the Kitchenaide fridge this stuff sloidifies in the water line and these things are not harmful. On the other hand, a neighbor who is in the toxic waste business took a sample and one of their chemist and at first glance the chemist said he, "thinks it’s something organic(carbon based). If it comes out of the water and doesn’t become soluble when the water is heated back up, it must be coming from your lines or your filter. He said he doubts it’s in the water. So, at this point I guess my only option is to replace all the water lines in the fridge. Is this something that a hand home owner can do or do I need the service of a professional for this? Thanks in advance.