Another classic moment from Garak. Wish we saw how this scene (from DS9 4x26) started! I reckon one of those guards dared the other to ask Garak if he was really a Cardassian spy, and Garak was just like “No my dear boy, I am just a simple tailor…” and then lays the tailor act on thick to wind them up. His attitude at the end is just glorious!
If you look at any situation throughout the series in which Garak is at a disadvantage (attacked by hostile Klingons, captured by Jem’Hadar, or in the hands of Tain), Garak’s whole mode is to not fall into one of the normal responses expected of a person in such a situation. One such response is to react with some level of fear. The other response is to be either passively or actively antagonistic. Instead, Garak engages in humor or calm chit chat and thus signals to his opponent that he is not going to let them control how he responds to the situation.
The security guards may not have said a single thing. But for Garak to simply be silent in response would mean the guards are eliciting one of the possible reactions expected of someone in such a situation. So I would expect him to the be the one who initiated the conversation. Regardless of whether the guards say anything in response, Garak has taken a measure of control over the situation.