Oh man, I LOVE this question!!
Your situation can actually be used as a perfect example of how to get your way without giving her an ultimatum. Obviously you don't want the pictures up, right? But, as I'm sure you're aware, if you tell a girl straight up to just get rid of them, she is likely to fight you on it, especially since she's new (only 2 dates in) and therefore you don't really have the built-in time with her or authority yet to say anything.
So, here's how you get her to take down the pics:
1. Date her for the next 2 to 3 months. Don't ever bring up the pics on Facebook AT ALL.
2. During this time, don't bring up any verbiage about you two possibly becoming a couple. Take her out once a week, show her a good time each time, limit your texting/calling/messaging to her and - most importantly - do NOT push for a relationship.
3. Assuming you're doing the right things (and if you don't know what those things are and aren't, click
HERE to start learning) and not asking her to be the girlfriend, her interest will build up enough in you to where she will be the one to bring up the issue of being BF/GF. Something along the lines of "So... what are we?" or "Where do you see this relationship going," etc.
4. When she brings this up... even if you like her and want her to be the girlfriend, DO NOT GIVE HER A STRAIGHT UP "YES." Instead, you go into what I call the Negotiation stage - this is where you iron out the details of what being in a relationship with each other means. During this conversation, you ask her what her expectations would be, as well as what yours would be. Most importantly, though, this is where you ask her questions about things she's doing that you do NOT like to see if she's going to continue to do them in the relationship.
And THIS - my friend - is where you bring up the pics.
Because at this stage she sees you as important enough to be in a relationship with, which means she not only respects your opinion, but WANTS to respect you because you've now EARNED it. So, if she's doing things that are somewhat displeasing to you (like having up pics of the ex), these are things that, upon having them pointed out to her and finding out that you won't be in a relationship with her if these things are happening, she will be willing to change if she really wants to be with you.
Here's an example of how the convo would go:
HER: So... what are we?
YOU: What do you mean?
HER: Well, we've been dating for 3 months... I'm not seeing anyone else, are you?
YOU: Well... no...
HER: Sooo... should we take things to the next level?
YOU: Hmmm... well, it depends: if we start going out, are you still going to be the sweet loving girl you are now?
HER: Oh, absolutely! (It's a lie, but let her get away with saying it)
YOU: Okay... does this mean you'll take ME out now for the occasional date night?
HER: Oh sure - I'd love to plan a night out sometime
YOU: Hmm, okay... let me ask you: do you currently have any ex-boyfriends you hang out with or talk to on a regular basis?
HER: Well, only Bob, but he's harmless, and I dumped him, remember?
YOU: Okay... and what about your FB pics - do you still have pics of yourself with exes up on your page?
HER: Well, I think maybe a few, like 5 or 6...
YOU: Hmmm... well, maybe we should just keep things the way they are for now
So, what you're doing at this point is telling her that as long as traces of exes are lurking in her life (via pics, conversations, etc.), that a relationship with her is not going to work. You're not TELLING her directly to get rid of these things - after all, nobody likes to have their free will challenged - but you're simply saying that her having those things in her life won't make a relationship work for YOU. Which will let her know indirectly (because women are GREAT at reading passive behavior) that you're saying "no" to her request for a relationship unless she gets rid of these things.
Now, when you first do this she'll probably try to do some female reasoning with you:
HER: But why? You're the one that's most important to me, I don't really care about those other guys anymore!
But, you have to remain firm in your resolve. After all, she needs to be the one to know that if a relationship starts it's going to be on YOUR terms, one of them being that the pics come down and the exes gotta go. But again, not directly:
YOU: I hear you... But still: for now, we can just keep things the way they are.
And that's it. No explanation needed, but it will let her know where you stand with her having exes in the background without "forcing" her to do anything. She'll probably seem mad initially, but more likely than not she'll come back a few days later with "Okay, I got rid of the pictures, can we PLEASE talk about us getting more serious again?"
(NOTE: This also applies if you're dating women online - sometimes after you've been dating for a few months a woman will want to move things to the next level but still have her profile up online. That's when you hit them with the question "Hmm... well, is your profile still up on the dating site?" If the answer is yes, same answer: "Maybe we should just keep things the way they are then..." TRUST me, it makes 'em take down their profile quick!)
Hope this helps!