Rats have a tendency towards tumors. That's why labs use them so much. Certain lines are bred distinctly to have cancers, in fact.
Cancers and mammary tumors do not spread. They are not contagious. Now, will her babies have more of a chance to develop cancer/tumors? Hard to say without knowing which type of tumor that is.
Most likely, you won't see any higher number of tumors in her offspring, but if so, then you can begin culling them out of your colony. Right now, you admit you can't tell her offspring from the others.
If you can keep a record on who is who, it will help the breeding program down the line. That way you can tell who have larger litters, faster growing offspring, less weight loss after birth... etc.