The only correct way to solve the problem is by directing the exhaust outdoors instead of into your new "room."

Any sort of lint-catcher placed on end of the duct would quickly get clogged with the lint and obstruct the airflow (unless it's cleaned often).

Agree with DaDoes. You should vent it outside. In the meantime you could try pantyhose over the end of the pipe or a stocking would be easier changed. Dont let it get clogged. Better for you and your family exhausted outside.
I have also seen a thing that fastens to your vent hose and you fill it with water and the water catches the lint. Not sure how good that would work but they do make such a thing. That or the stocking could get you by till you can reroute ductwork.

Please tell me this is an electric dryer.

Thanks, all! Very helpful :)

You might be able to install one of FanTech's lint traps into the wall and make it look nice? They are made to go along with a FanTech booster, but a lot of folks use them under decks to cut down on lint. It is not ideal, but it might be an option.

Here is a link that might be useful: FanTech Box on Amazon

Can you use a hole saw to cut a 4" hole in your deck. Then you can run a vent pipe under the deck and the only visible eyesore would be the angle bend and pipe going down. Only would work if your deck is wood or simulated wood frame construction.

MizLizzie, thanks! I actually found that exact one on Amazon...looks like a possibility. And nerdyshopper...great suggestion but we have a slate floor on the porch so we need to trap the lint directly where it exits house.

Since most of these units seem to use water, we tried placing a container of water under the vent and it did make a difference! Might be the best cheap-o solution :)