The main reason in which the Czech government-in-exile decided to go through with Operation Anthropoid was to show the Allied powers that the Czech government is indeed anti-Nazi and is playing its part in resisting them. A lot of government-in-exiles used assassinations and various attacks on either military units or government facilities to claim legitimacy and be able to say "Hey, we played a role in fighting the Central Power, so we'd like some recognition." Assassinating Heydrich was what the Czechs decided to do exactly that.