Proving that a set of grammars for a given finite language is decidable
Hint: Combine the following two properties of context-free grammars:


Given a context-free grammar $G$ and a regular language $L$ (given by a DFA, say), there is an algorithm that constructs a context-free grammar $G'$ satisfying $L(G') = L(G) \cap L$.
Given a context-free grammar $G$, there is an algorithm deciding whether $L(G) = \emptyset$.