  Bringmann, Guerzhoy and Kane have shown how to correct mock modular forms by
a certain linear combination of the Eichler integral of their shadows in order
to obtain p-adic modular forms in the sense of Serre. In this paper, we give a
new proof of their results (for good primes p) by employing the geometric
theory of harmonic Maass forms developed by the first author and the theory of
overconvergent modular forms due to Katz and Coleman.
