It’s not very long before Duncan calls back. Laird took his interest for the other thing it was—a hope that they could use the Charybdis as a generator or a means of preparing retroactively—and shot him down as expected. But as for what it “eats,” Laird has been theorizing.
From its point of view, time is a directional force. When the Charybdis swallows something, that thing moves through time by the monster’s rules instead of the rest of the universe’s. Then it expels it, and derives its energy from its meal (or more likely its meal’s corpse or fossil) being pushed back by normal time passage. It’s much the same concept as someone who finds himself immune to gravity creating free energy by bouncing up and down a ladder and releasing heavy objects to become normal at the top.
Laird is like 80% sure this is what’s going on. Duncan notes that if true it does mean the Charybdis gets some small benefit from giving Sadde a short-term ride to the past, but has no idea whether it’d see that as enough of a bribe to be worth doing.