Use a white soft cloth with a tamping brush pad action. Some furniture stains may be removed with a stain, oil, and grease remover. A citrus solvent spotter may remove varnish and oil stains on colorfast carpets. Debrowning agents often help with tannin stains. A mild rust remover is often successful in removing rust stains.
Some spots are actually mold and require treatment with an antimicrobial or sanitizer.
If the stains are successfully removed, a rinsing of the agent followed by a total cleaning of the carpet using the proper detergent or shampoo is recommended. Unfortunately, many times there has been a permanent stain transfer and replacement may be the only viable option. If you live in an area vulnerable to hurricanes, consider installing storm shutters. Also, consider the width of the window, as it may be necessary to nail 2x4 stiffeners to the shutter panels to reinforce them and prevent flexing. Measure and cut your plywood shutters to fit the windows, then mark them so you'll know which window they fit.