At one point in me and my fiances relationship, before we were engaged, I had friendships that were similar to what you describe. To be honest, my intentions were not that good. Nothing happened, but I'd fantasize about it, and I wanted them around to experience the excitement they brought. I'd go out with them and actually do stuff. Me and My fiance don't do stuff like go to bars, or spend time with groups. With those past friends, I did. Hanging out with them in environments that were not great (like bars) late into the night, and talking to them constantly filled the void of my otherwise boring life.

It's obvious that she is enjoying the attention and such from this friend. Who wants to give that up, really? But you question the friends intentions. The thing is, is I don't know exactly what your concern is. Are you concerned this relationship is potentially romantic or sexual, or becoming that way? Are you just concerned that this person is becoming stalker-ish in your point of view? What type of inappropriate conversations where they? There are a lot of ways that they could be inappropriate.. particularly if they were romantic conversations, but that isn't specified, so it's hard to pin point what would be a justifiable route for you to take.

The thing is your wife is enjoying the attention and companionship. If those conversations are solid evidence of misconduct against your marriage, you would have reasonable cause for wanting them to significantly tone down and/or end their friendship. And you should take that route. If not, there is no way you can really tell her to stop if she already said she wont. Not without making her feel like you are abusing your rights as her partner and trying to control her. You will likely have to wait awhile to see what ends up happening. It is possible something more will happen that will re-affirm that they need to tone down/end what they are doing.