Should I replace this winch hook?

I'd like to see the clamps they used on the wire rope.

But yes, the WLL should be cast into the hook. That one is just a farmer/hardware store hook. Also, you must have a thimble. The strain on the cable is the weak link right now. And how are the wire rope clamps connected.

But first, you need to cut off the loop thru the hook, get a rated hook, use a thimble, and install 3 clamps correctly.,
a standard eye is acceptable, thimble eyes hold up better to wear but not required.
 
I understand the difference between winching and hoisting. It seems a simple enough winching maxim to say, "Pay attention to the breaking strength of your winch rope and the load limits of each component as affected by the manner in which each component is being used and remember that the system is no stronger than the weakest piece." However, the fact that shackles, hooks, etc. have designed safety factors in excess of marked working load limits seems to be mentioned in every winching thread and the implication is frequently that winch rope breaking strength and stamped WLL markings can be exceeded with impunity because of those safety factors..

If design factors don't apply to vehicle self-recovery with a winch why are design factors always mentioned? Why are these safety factors mentioned by companies in the winching business who we should expect to be able to rely upon as experts? That's what confuses me.

Speaking only from the hoisting or industrial side, one never exceeds the SWL (safe working load) of a crane, hoist, rigging, etc.. Yes, there are design factors that give a factor of safety but we never worked in those areas.