I've done the Cleveland Way a few times and never had a problem with high tides, guess I've been lucky.
But, according to Paddy Dillion's Cleveland Way guide book, that if the tide is in, is retire to the pub at the top of the bank and spend 1 or 2 hours in there until tide go's back out. But, another guide book by Malcolm Boyes, said the beach between Runswick Bay and Hob Holes, is one of the few places where it is possible to walk safely along the beach at high tide.
One alternative route is, head up the lane from the pub towards the A174 and turn left for a 1/3 of a mile, to GR:800 144, look for a public right of way, that will take you to Coverdale Lane, now head for Westfields farm, another path will bring you to the disused railway line and back to the Cleveland Way @ GR: 821 153.
But, can't see it being a real problem. Anyway, you have 2 choices, either the pub or alternative route.