Garak knew that he might have to assassinate her someday. It would make his innocence much more plausible if it was clear they’d never had any interaction with one another. Besides…

“Would a simple tailor assassinate a Kai?! Oh come now constable, I’ve never even talked to her. Oh, I’d see her from time to time crossing the promenade, but if that were the only thing that would qualify me as an assassin, then you should lock me to protect the life of a quarter of Starfleet’s finest officers, not to mention entire Bajoran delegations, Klingon High Council members, and the Grand Nagas while you’re at it. Now really constable, I respect your authority on this station and wish you luck in your search for an assassin, but I have a customer that needs an urgent hem for a dinner party tonight.”

Pauses for a moment and looks Odo up and down

“If you’d like me to take look at your uniform, I could fix that hem too”

as Odo looks at his feet Garak disappears