Sure you can get rid of it. But you have to 'find' the source.
Once you've located the mold/mildew, you can use a mixture of 1 cup of Household Bleach to 1 gallon of Water. If you need a stronger solution, double the Bleach to 2 cups, or more. (Do wear gloves and have a 'planned' way to ventilate while you're spraying!)
Spray the solution on w/a spray bottle and let it sit for 5-10 minutes. Then, spray again, and let it sit again. Then spray a 3rd time and wipe (and rinse whatever you're using to wipe.) Do keep your 'clean water' bucket filled with CLEAN water. Otherwise, you'll simply xfer the mold/mildew back on whatever it is you're trying to clean. Clean from the BOTTOM, up; NOT the top, down. If you clean from the top, down, your 'cleaning work' will cause 'runs' and it will leave streaks behind. And when you're ALL finished, empty the bottle and just rinse and wipe with CLEAN water. (Then throw away the bottle since you had Bleach in it.)
Keep a mixture around in a gallon container that is WELL sealed (to keep kids out of it), and WELL labeled (for all to read.) When you get the 'smell' of M/M, pour some in the pit a few times until the pump has run the water through it.
As an aside, keep your eye out for future signs of M/M. It CAN return to the surfaces you've cleaned! If this is the case, you'll have to clean them again AND consider getting a Dehumidifier. Be sure you eliminate the sources of M/M from the basement. Things like venting your dryer vent in the living space are a no-no. You shouldn't have to do anything like 'vent' the basement. A totally enclosed/sealed basement can be controlled. Understand that M/M are caused by the right combination of the following 3 things: Moisture, Temperature, and Little-to-No Sunlight. If you can eliminate or dramatically alter just 1 of these 3 'conditions', your problem may go away. Alter each and every 1 of them, and the odds increase.
My best to ya and hope this helps.
Jay J -Moderator