In this paper by Ambainis, he talks about the applicability of Grover's Search to Schöning's algorithm for solving the 3SAT problem to obtain a runtime of $O(\sqrt{1.329...^n}$.
In the original algorithm by Schöning, the algorithm is repeated for $1.329^n$ time to obtain a constant success probability. Ambainis states the following: "To obtain a quantum algorithm, we just use quantum amplitude amplification instead of classical repetition."
I don't understand here at what stage we apply Grover's Search. For instance, what is the search space on which we are applying Grover's Search?