Can sea turtles feel it when you touch their shell?

Yes, sea turtles can feel it when you touch their shell. Sea turtle shells consist of bones, which are covered by a layer of so-called scutes (plates). These scutes are made of keratin, the same material that human fingernails are made of. There are nerve endings enervating even the bones of the shell. These nerve endings are sensitive to pressure, for example from a touch on the back.

Drawing of green turtle shell showing 4 pairs of lateral scutes, graphic — Green turtles have 4 pairs of lateral scutes.

A green turtle swimming in the blue ocean with four pairs of lateral scutes clearly visible on the shell, image. — A green turtle with the lateral scutes clearly visible.

References:

Thomson JS 1932. The Anatomy of the Tortoise. Scientific Proceedings of the Royal Dublin Society.
Zangerl R 1969. The turtle shell. In: Gans C and Bellairs A (eds.): The Biology of Reptilia, Vol. 1: 311-319. Academic Press, New York.