You strip off all proteins on the cell surface by using a protease (an enzyme that destroys proteins). Now, when you add a specific signaling molecule, the cell still responds. What is the most reasonable explanation of this?

When a specific signaling molecule is added to a cell whose cell surface has been stripped off by proteins the cell still responds because the receptor is in the interior of the cell.

Receptors are divided into two categories which are;

Intracellular receptors or internal receptors which are found in the cytoplasm or nucleus of the cell. They respond to hydrophobic ligand molecules which are able to travel across the plasma membrane
Cell surface receptors which are found in the plasma membrane

Signalling molecules are necessary for the coordination of cellular responses by serving as ligands and binding to cell receptors.

A type of signaling molecule are the small hydrophobic ligands which can directly diffuse through the plasma membrane and interact with internal receptors unlike the water soluble ligands. This is why the cell still responds after you strip off all proteins on the cell surface.

NOTE: Nitric oxide (NO) is a gas that also acts as a ligand, therefore it can pass through the plasma membrane of the cell and interact with receptors.