N.Y. CPLR 1336
A defendant enjoined by a preliminary injunction may move at any time, on notice to the claiming authority, to vacate or modify it. On motion, without notice, made by a defendant enjoined by a temporary restraining order, the judge who granted it, or in his or her absence or disability, another judge, may vacate or modify the order. An order granted without notice and vacating or modifying a temporary restraining order shall be effective when, together with the papers upon which it is based, it is filed with the clerk and served upon the claiming authority. As a condition to granting an order vacating or modifying a preliminary injunction or a temporary restraining order, a court may require the defendant to give an undertaking, in an amount to be fixed by the court, that the defendant shall pay to the claiming authority any loss sustained by reason of the vacating or modifying order.
N.Y. CPLR 1336