How to edit a Mecanim animation for your character?

Maybe this seems like a really simple question, but I can't seem to find the answer I'm looking for. I have my character set up for Mecanim and I downloaded the Raw Mocap Data asset from the asset store. I am using one of the idle animations for my character, and it looks great right now except for one thing. The fingers are shaped really weird when I apply an animation. It happens with any animation I apply to the character.

Here is a picture of the character with no animation attached, just in the T-Pose. The fingers are just fine in the original model/pose.

And then here is a picture of the character with an animation attached (this one is the idle animation):

See how the thumbs and index fingers are curved strangely? Is there a way to fix this, preferably without editing every single animation I put on the character? Or if I do end up needing to edit every animation, how do I go about this?

Thanks in advance for any help.