Yes, it's done via ROV's with manipulator arms that attach salvage cables to them. Way less failure prone than trying to bring them up with the ROV's directly because the ROV's are normally tethered via a fairly light duty tether that's connected to a base station that raises/lowers the craft. That keeps things much more maneuverable because the ROV doesn't have to drag around thousands of feet of cable, and, it provides some damping from any movement of the host ship operating it.

Additionally, the ROV can stay submerged, looking for other things to grab, while salvage cables are raised/lowered. Doubly important because those sorts of winches run at ~1000ft/hr, and the wreck is ~12.5k feet down, so over a full day for one recovery.