From the days of wooden boats and iron men:
To trice-up is to tie-up or hoist with a small rope; it can refer to tricing-up a sail, or tying down deck cargo. In the case of a tender on davits, it is the practice of supporting the tender with ropes chris-crossed underneath typically attached to the tip of the davits and to the transom. This provides both support and reduces movement in rough waters.
On the PDQ 32, a pair of 25-foot dock lines I reserve for cruising are just perfect, serving 2 purposes. They are looped over the cleats on the davits, through the welded eye at the tip of the davit, and secured back on the cleats. The complete process takes about 1 minute.