Remorse cooperates only if it is in bad standing, or if both players cooperated in the previous round. In other words, Remorse is more aggressive; unlike cTFT, it can attack cooperators.
Against the strategy “always cooperate”, cTFT always cooperates but Remorse alternates cooperating and defecting:
C/C → C/D → C/C → C/D …
Shouldn’t the second one of these be C/C, since one player is “always cooperate” and the other player cooperates “if both players cooperated in the previous round”?
Yes. Page 287 of the paper affirms your interpretation: “REMORSE does not exploit suckers, i.e. AllC players, whereas PAVLOV does.”
The OP has a mistake:
Remorse is more aggressive; unlike cTFT, it can attack cooperators
Neither Remorse nor cTFT will attack cooperators.