I went through a similar situation with my daughter. First of all, I think it's wonderful that you don't see Girl X as a bad kid (at that age it's never their fault). I had to work hard at this with "Our Girl X" (let's call her OGX). My DD was 6/7 at the time (it was grade 2).
There are two ways to look at it. One is that less than desirable situations provide learning opportunities. This was my original approach - I would discuss "OGX's" behaviours with my DD, while trying to be compassionate towards OGX (keeping in mind that my DD loved this kid). The second way is to restrict your child's access to influences you you don't like, which is what I ended up doing. In the beginning, though, I tried talking my daughter through it.
For example, OGX was a liar (I caught her several times). DD and I would talk about lying and how it's wrong, and isn't it sad for OGX that she hasn't learned that yet. OGX was very rude as well, blatantly refusing to say "please" and "thank you" even when gently reminded. Again, this prompted conversations with my DD. OGX had less than desirable morals, as well: one day she and DD were picking up litter in the school ground... DD said her reward for this was helping the earth to be greener, and OGX said she wanted to be rewarded by being on TV.
Omgosh... AAND (I'm remembering more now, lol), OGX would purposefully chew with her mouth open because she knew it annoyed people, AND she used to brag about using a calculator to cheat in math. One day at our house we had a coin toss to see which girl would get the first turn on the computer and OGX lost the toss... she also lost her temper and started throwing stuffed animals at me.
(sigh)
It got to the point where I was SO tired of the "crisis management" conversations. The scales had tipped from "learning opportunities" to "excessive bad influence." When I noticed my DD starting to pick up on OGX's behaviours, I finally put my foot down and created distance between the girls: fewer and fewer play dates between the two of them, and proactive encouragement of other friendships.
Now the situation seems to be resolved - they both have other friends and they're both in different classes.
My advice would be to find your own balance between learning opportunity Vs. bad influence. Set up play dates with other kids, and be proactive about filling your DD's schedule so she doesn't have as much time to spend with Girl X.
Good luck
