Following the fatal man overboard accident in November 2017 during the Clipper round the world race the Marine accident Investigation Board has issued a safety bulletin (
https://www.gov.uk/maib-reports/safety-warning-on-the-use-of-safety-harness-tethers-on-sailing-yachts ) concerning the use of the tether hooks on the end of Marine lifelines. In summary, if the lifeline runs under a cleat or similar bit of deck hardware so that, if you fall, the force on the tether-hook is not in line with the hook, it may give way so you are no longer tethered to the boat. They recommend checking where you tether yourself to, and making sure that sort of thing won't happen.
I must admit I've never liked the sort of hook they put on the end of marine lifelines since I find them clumsy to use. I prefer to use a screw-gate carabiner similar to the ones I used to use in my previous existence as a troglodyte (in the cave dweller sense!). However be warned that the type of modern carabiners used by rock climbers are probably not suitable for our purposes being made of light alloy which may not get on well with sea water. On Seatern I use the chunky marine stainless ones of the sort you can get from chandlers.
Peter