In a small non-reactive pan, heat the white wine vinegar with the garlic very gently over low heat for about a minute. Leave to infuse for a few minutes. Strain.
Stir together the melted butter and strained white wine vinegar. Squeeze in the juice of a quarter or half a lemon.
Season with salt and pepper. Taste. Adjust the amount of lemon juice, salt, pepper or all of them, if needed.
To assemble the dish: Lay the poached fish on a serving platter. Drizzle sauce over the enter firsh. Arrange the olive slices on top of the fish. Sprinkle with mint leaves. Serve.