Sorry to hear of your water problem. Yes, wash as much as you can and quickly to avoid mildew. You could use a rotary cutter with a pinking blade to minimise raveling.
You might also try to paint the basement walls with paint that keep water from going thru. But even better is getting the fabric away from the walls. Or you can move it up stair away from the basement.... Let us know what you do hand how well it works. I wish I had a basement...... No basement, cement slabs... I live to close to the water even tho I don't have a lagoon near me.