I think a little bit of jealousy in a monogamous relationship is normal. It's a normal reaction to a real or perceived threat to the relationship (studies on polyamorous couples have actually found that the incidence of jealousy tends to be much lower -- because even if a partner leaves, the remaining partner still has other options. The emotional blow is reduced).
But, that gets into the meat of -- what's justified jealousy? What's a normal amount to deal with, and how much is too much?
I'd say that a couple healing from an affair...it's justified for the girlfriend or wife to feel insecure and worried if he gets a text from an unknown woman. I'd expect him to explain who she is, and even to offer to let her read the messages as they try to move forward.
Unjustified? I have a cousin whose girlfriend will not let my cousin talk to other women at work. It's so extreme that the girlfriend has told my cousin not to apply at jobs at certain places because there are "too many women" or "too many pretty women." That's just ridiculous.
Those are both extreme examples. I don't know what this woman said to OP's boyfriend. Was it just a, "Hey you!"? Does she comment on everything he posts or send him flirty messages? How much control does OP's boyfriend have over the situation -- since he works with this woman, presumably he doesn't want to make it awkward and may find it's better to just deal with flirtatious messages. If that's the case, I'd hope he would talk to his girlfriend.
OP didn't indicate, but I'm not sure if she even asked him to delete this woman from Facebook. Maybe she did (maybe I missed it?). It sounds like he just jumped to that as a solution, although again, I'm not sure.
I'm married to my husband now but we went through an awful period while we were dating. Now that I'm older and wiser, I would have just left rather than be put through that kind of anxiety and jealousy again.
Men get jealous too. I don't think the solution is to automatically dump a partner if we feel jealous or believe the problem is strictly with us. It certainly can be. I liken jealousy to many other emotions -- anger included. I've certainly been angry with my husband in the years we've been together. Jealous, too, in both directions.
There is a point where jealousy becomes pathological and it is a huge problem...just like people need intervention for their anger. But where that line is, I can't say.