Hydrolyzes iota-carrageenans, sulfated 1,3-alpha-1,4-beta galactans from red algal cell walls, with an inversion of anomeric configuration. Also active against hybrid iota-/nu-carrageenan, not active against kappa- or lambda-carrageenans. Endohydrolysis of 1,4-beta-D-linkages between D-galactose 4-sulfate and 3,6-anhydro-D-galactose-2-sulfate in iota-carrageenans. Belongs to the glycosyl hydrolase 82 family.