Rust on Bottom Edge of Door

The bottom edges of my doors are rusting. This is the only rust on the vehicle, and it seems to be caused by the weatherstripping that's on the door bottom. It's a strip that's rivited on, and it retains moisture for several days after a rain or wash job.

Can I remove the bottom strip with no ill effects, or is there a better solution to prevent the rust?
Thanks for any ideas.
Don
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1989 XJ Sport 2-dr, 4.0L AW-4

that could be the cause...
but usually what i have seen is the vents/drains in the bottom of the door get clogged and hold water inside of the door then rust will form around the pinch weld of the door....once it is rusting there, it is all over but the crying...
pull your door panel and look inside the door around the bottom check to see if water has been standing... if it has then clean it really good with a wire brush inside and out, then use a conversion coating such as P.O.R. to line the inside with... and possibly the outside too... and make sure the drains are open...the rust is next to impossible to stop after it starts due to the double layers of metal in the lower lip of the door...

Thanks, xjhm. You're probably right, because the rust goes all along the bottom seam. I'll pull the door panel and take a look. I don't have a good feeling about this, because it looks like a tough place to repair.