Hello! Well, I've had a similar experience in the past, and here's what I learned. Just because our water is clear doesn't mean something is wrong somewhere. I too would have to hose-out my filter everyday, sometimes 2-3 times per day hoping it would filter-out the algae. But it doesn't work that way. The reason algae finds that lovely, dark, cozy home is because it's just that - perfect for algae. Also, your chemical balance (chlorine compared to CYA/stabilizer) is probably not correct. When the chemical balance is correct, your filter will not have green in it.
Best thing you can do for us right now it provide a full set of test results (FC, CC, CYA, TA, PH, and CH) via your Taylor K-2006 or K-2005 w/ FAS-DPD test. If you do not have one of those test kits, you must get one right away to provide and monitor the FC, CC, and CYA accurately and at higher levels needed. Let us know if you have any questions.