Clutch Hand Strap
Capture's plate (any model of plate that we've ever sold) has loops in it for attaching Peak Design Anchors. The Anchor can then connect to your Clutch hand strap, or for that matter any Peak Design strap.
3rd Party Hand Straps
Some hand straps, like those made by Spider Holster, are designed to work with any tripod plate. Those will work great with all Capture versions. Otherwise, you cannot use a standard (1/2 inch wide webbing) camera hand strap with Capture at the same time.
Way back when we supported this functionality (see image below). The original Capture v1 had a quick-release plate that contained 4 strap loops explicitly for the purpose of connecting to 3rd party hand straps. This feature, however, was discontinued in 2013 because we found that standard hand straps often obstructed use of Capture by getting lodged between the clip and the plate. Additionally, we found most camera hand straps to not meet our needs...they were bulky, floppy, hard to adjust, and ugly. Hence we developed our own hand strap to solve those needs, as well as integrate seamlessly with Capture.