Pete's logic has some big leaps to it, though. First, the notion that a shot would be limited to lightspeed when FTL is a thing, hell the thing that started this line of thought was receiving an FTL message. Second, even if the beam does travel back through time, he assumed it did so at a one-to-one rate for no real reason. And finally he's using out-of-character knowledge.

I really don't see how the GM could have expected them to figure that out, when time travel had never even be a part of the setting beforehand!