Eavesdropping on everyday conversation doesn't do it for me thanks to my deep-seated hatred for small talk, and I don't see the point of it because it's boring, unstimulating and random while adding nothing to my already extensive pool of knowledge.
You are closing yourself off to understand the purpose of small talk. Personality and connection. In real life, people use small talk as a means of "assessing their surroundings and the situation". You familiarize yourself with the personalities and emotional state of others in the conversation. It isn't what is said, but how.
Others have already mentioned that the dialogue is a bit stiff and a little awkward, but I feel like there are two big things that cause that. The awkwardness could be partly explained by context. Maybe the characters are from different cultures, and the speech pattern is meant to match a different language or something like that. The stiffness issue however, I think comes more from the amount of exposition being directly dumped into the dialogue without any breaks.
This short bit of dialogue gave me so much information that I am a little lost in what is actually going on, and more just trying to keep track of what they are talking about. The characters don't have to actually say everything they are thinking, and a massive part of communication is body language and visual cues, as well as tone of voice. Those things probably count for more than the actual spoken words themselves.
Try breaking up the dialogue by inserting statements about the way things are said, or how the characters are physically reacting to statements. You can include internal thoughts between statements as a means to convey a more detailed idea, without them actually saying things that don't really need to be said.
Honestly, the only truly stiff parts of this dialogue are the male character's lines. the first statement sounds very pompous by first saying something is impossible and then immediately saying the speaker has never known something, which feels like it implies that he thinks if he hasn't heard of it, it must not be possible. The questions then are actually giving more information to the other speaker than was every implied, and they come out unnaturally because a normal person wouldn't do that.
The woman is making an assumption and the man is directly confirming it by not only saying that he is Irish and Greek, but offering that he is half of each. From the woman's statements all she necessarily knows is that the man has some ancestry in those cultures. It could be half, or it could be a quarter, or it could be an eighth. Dormant traits have been often known to surface two or three generations down the line. A more natural response would probably be a silent, physical reaction, followed by a more cautious question. The whole thing might be something more like:
“B-but that’s ridiculous! I’ve never even heard of the Picts being dark-skinned or having Scythian tats!” He thought the idea to be laughable.
“Funny, because I also do not recall Érainn to have such a lovely skin tone like yours." she said with an almost flirtatious wit, "And If I were a guessing girl, I would say that you have Gréagach blood in you.”
He stiffened at the accuracy of her statement. He wondered how she could possibly know his heritage, they'd only just met.
“You are an odd creature." she said with a smirk and a glance that felt as if she were peering into his mind, "A man who refuses to acknowledge his warrior heritage, the Érainn blood running through your veins.”
“And how do you know anything of where I might come from?"
She didn't answer at first, only watched him as if gauging how best to respond. Then she smoothly shift her hips and slowly stepped across the room.
“Well, you have that crimson hair common amongst your kind, and I have heard wondrous tales of a wise, noble people living far beyond Alba with mud-brown skin who call themselves Gréagach. Does that answer your question?”
I added a bit to the scene, but I needed to fill in some details so I did my best to assume. It is just an example of course, but I hope it helps you to understand a little bit better how to carry the scene. At this point the only information we really lost is the specifics of being half Irish and half Greek, but that detail isn't really important to the scene at all, and likely something that the reader would already know or could easily learn later in the story if necessary.