  For a del Pezzo surface of degree $\geq 3$, we compute the oscillatory
integral for its mirror Landau-Ginzburg model in the sense of
Gross-Hacking-Keel [Mark Gross, Paul Hacking, and Sean Keel, "Mirror symmetry
for log Calabi-Yau surfaces I". In: Publ. Math. Inst. Hautes Etudes Sci. 122
(2015), pp. 65-168]. We explicitly construct the mirror cycle of a line bundle
and show that the leading order of the integral on this cycle involves the
twisted Chern character and the Gamma class. This proves a version of the Gamma
conjecture for non-toric Fano surfaces with an arbitrary K-group insertion.
