In that case, I think the above 1851 Census index covers that area and unfortunately the people mentioned aren't in it.
New Marske didn't really amount to any size whatsoever in 1851, in fact on an old map from 1857 it isn't even marked. The link below will take you to a map for 1857, somewhere near Redcar, follow the railway line heading south and east and you will eventually come to Marske-in-Cleveland. todays New Marske is sited south of the railway line, between Marske and Upleatham, which lies to the south of Marske.
There is a possibility that they came under the 1851 Census index for Kirkleatham and Upleatham, which unfortunately I don't hold a copy of.