Any sense of what the contaminant is? Knowing could help guide for selective enrichments and/or isolation. I would first take a stab at plating them at high dilutions and looking for potential morphological ways to distinguish and isolate. Or you could just isolate a lot of the colonies, grow them up sterile and have them ID'd for final confirmation before you regrow them.

Is it a pure or an enrichment culture? If it was a pure culture of single SRB, to clean it is a very simple - just obtain colonies under microscopic morphology control and/or other control methods and recover pure culture. If it is an enrichment culture with lots of SRB, it's a bit more difficult... In this way it is necessary to maintain species number of SRB, I think. In my opinion, the first and the simpliest way to recover clean SRB culture is to find old clean sample used before contamination and try to regrow it.

If the identification of a contamination agent is necessary, You need to obtain its colonies under aerobic conditions and make all needful identification procedures (16s rRNA sequence, biochemistry/physiological testes etc.). And after that just to try find a way to eliminate it. But it is a bit complicated procedure.

But, do You have the information about presence of aerotolerance among Your SRB? Or obligate satellites?

If your SRB are strict anaerobes and your contaminant can grow anaerobically then your main options are those of Dr. Flannery which means either culturing on a selective media to reduce growth of the contaminant.  But since the contaminant may still be alive, but not growing, you need to do dilution plates for isolation (either streak or pour plates).  Otherwise if you are not aware of the contaminant's id then doing the isolation plates until you obtain a pure culture of your SRB is the main method that I am aware.