You should have seen me scooping the intake out when I was changing the filter... going... WTF? How? Why? Huh? !!!!!!
At my parents house, the squirrels ate the gate right off of the fence (it was wood, now they've replaced it with a steel gate that looks like wood). They lick the salt off the bricks on the walkway outside their front door. Last Christmas, one kept unscrewing the Christmas lights outside the house and burying them in the flower beds. They caught him with a video camera because they couldn't figure out WHY their lights kept disappearing. They thought someone was playing a trick on them. Squirrels can be some crafty little bastards.
... so get an intake and get rid of that stock Habitrail hamster cage. It doesn't have to be expensive. My CAI came from eBay and cost $36 shipped. It's worked out great.