There are really two ways to look at this. In the end, you need to examine the situation, and follow your instincts.
The first way to look at this is that it's a temporary situation. The "biter" is going through a phase, and it won't last forever. If you generally feel good about the care your child is receiving, there is no need to remove him. There are "biters" at daycare centers, too. They're obligated to report incidents to you (and the "biter" has more potential victims to choose from), but there is no guarantee your child won't be bitten or scratched just as often at a center. Unfortunately, it just goes with the toddlerhood territory.
The other way to look at this is that it's one of the drawbacks of an in-home daycare situation. They're often watching their own children along with yours, and they MAY (not always) let their own children get away with behavior that you wouldn't tolerate. As others have pointed out, they also don't have to follow the same strict regulations. They're not obligated to report incidents, so when you see bite marks and scratches, you question what's going on.
Personally, I have my children in a professional day care center. I had my oldest in an in-home situation for a few months, but I removed her. I feel like I have more control this way. I know they're not being plopped in front of a TV all day. I know they're only eating what I pack. I know the teachers can lean on each other when they get frustrated or burned-out. I know my children are engaging in organized learning and crafts. And I don't have to work around someone else's illnesses and vacations.
Lastly, I'm sure you've already done this, but talk to your son about it. Teach him to be assertive, and tell this girl to stop hurting him. It truly helps to curb the behavior.
Good luck to you!