When water backs up in your basement, whether it is contaminated sewer water or just a burst plumbing pipe, if it stands for more than 24 hours it is probably beginning to create mould.
Just drying out the drywall may not be enough. When drywall gets wet it usually swells and retains a great deal of water. You need to get rid of all the water, and dry things out as quickly as possible.
If the drywall is swollen, you should cut away all the swollen part immediately and get it out of the house.
This will also allow the wood behind it to air out and perhaps dry harmlessly.
If you see signs of mould, or smell that musty smell, you need to kill it.
Minor problems can be handled with a simply dish soap and water. Bleach is not recommended. But you need to try and get to all the little corners and cracks, and if the musty smell persists, you may even have to tear the wall, or at least part of the wall down. Follow this link for full details on cleaning up mould.
Fiberglass can be dried outdoors and re-used. In serious cases, especially when contaminated sewage water has backed up into your basement, you will have to bring in special decontamination experts. And not all contractors or renovators know much about de-contamination.
For more help and guidance check the CMHC web site and look for pamphlets like "Cleaning up after a flood".