They met in Emond's Field, but Moiraine plays the Great Game, and Thom was no mere unknown court bard.
The first long span Thom and Moiraine are in the same plot thread, they are at the Stone of Tear after Rand conquers it, and she confronts him to push him to act as escort to Elayne and Nynaeve. The conversation is full of implications and subtext, but the thrust is when she confronts him on his past.
Her smile was just short of laughter, but she spoke as if reading from a page. "Thomdril Merrilin. Called the Gray Fox, once, by some who knew him, or knew of him. Courtbard at the Royal Palace of Andor in Caemlyn. Morgase's lover for a time, after Taringail died. Fortunate for Morgase, Taringail's death. I do not suppose she ever learned he meant her to die and himself to be Andor's first king. But we were speaking of Thom Merrilin, a man who, it was said, could play the Game of Houses in his sleep. It is a shame that such a man calls himself a simple gleeman. But such arrogance to keep the same name."
The Shadow Rising, Chapter 17, Deceptions
Moiraine never makes any indications she knew Thom before, just that she knows his story. She knows about Owyn's death, and hooks Thom using information he'll need to avenge him.
This is definitely portrayed in this chapter as an aggressive manipulation, so it's not like they're cordial at this point or ever were. With all the subtext surrounding this manipulation though, is a wealth of information. Moraine's comments confirm she knows Thom is not just a master player of the Great Game, but also a peerless assassin, as well as someone with fierce loyalties. It's no accident that Moiraine brings up two Great Lords of Tear that opposed Rand in secret, and met with accidents themselves. She wants him to know that she's aware of all he's capable of. This wouldn't be necessary if they knew each other.
The subtler, deeper implication hiding behind all the obvious ones here is that she admires him for all these qualities. She ends the conversation by telling him that not all Aes Sedai are alike, and while Thom's reaction to her ploy tells us that she's just stringing him along, the flipside of this is that she may honestly want him to look on her fondly. The few fidgets she has during the conversation Thom interprets as hiding smiles or laughter to avoid insulting him, but are probably actual expressions of feelings she has for him. She just can't put aside her mission to indulge in those feelings.