It should come out. It's probably trash now, so stick something up there and rotate it around and break it loose. The fiche shows the filter sealed to the petcock with an o-ring.
My 2 cents: I've never been a fan of tank sealing. Neglected tanks rust. Tanks on bikes that are ridden and have relatively fresh gas in them typically don't. And I realize that is human nature to only remember the negative, but I don't remember seeing a sucessful seal job. I hear tell of 'em, but I also hear tell of Sasquatch. And these comments will surely bring out the sucess stories from the forum.
actually bikes that are parked in an area with temprature changes rust. In order for a tank to rust it must have water in it and although a protion of this comes from the water that is in your gas from the local pump (there is always some small amount), the majority of it comes from condensation formed in the tank by changes in temprature. Water is heavier than gasoline so the water settles to the bottom and the gas holds it there as it varnishes. I had a friend whose tank rusted on his daily rider because he parked it right next to his garage door and the temp changes from opening and closing the garage door when the rest of his family came in and out the house caused it to flash rust pretty fast, not as fast as if he left it alone with stale gas but it rusted none the less.
I used to work for a radiator shop and sealed gas tanks all the time. The reason you don't "hear" about a successful seal is that when it goes great people rarely post, but when it goes sour people post looking for help. I probablt have sealed about 50 gas tanks in my life and the only one that went bad on me was a rush job where I didn't prep the tank well and I used kreem (which I despise because I find it really hard to work with and because it breaks down in gas). If you can use Redkote or Por15, both are excellent products.
now to get this thread back on track:
get a pair of needle nose pliers and yank that old filter out of there. it is probably junk anyway at this point and if not it is atleast going to be clogged. If you pour the liner in there with the filter still in place you will render your tank useless as it will seal the filter up and not allow anything through. Since the tank liner is depending on your petcock to exit the tank, pushing through the filter out is going to seal it up but good.
after you have gotten it out, go to honda and order a new one, or run an inline aftermarket filter.