  Quantum corrections to the Schwarzschild metric generated by loop diagrams
have been considered by Bjerrum-Bohr, Donoghue, and Holstein (BHD) [Phys. Rev.
D68, 084005 (2003)], and Khriplovich and Kirilin (KK) [J. Exp. Theor. Phys. 98,
1063 (2004)]. Though the same field variables in a covariant gauge are used,
the results obtained differ from one another. The reason is that the different
sets of diagrams have been used. Here we will argue that the quantum
corrections to metric must be independent of the choice of field variables,
i.e., must be reparametrization invariant. Using simple reparametrization
transformation, we will show that the contribution considered by BDH, is not
invariant under it. Meanwhile the contribution of the complete set of the
diagrams, considered by KK, satisfies the requirement of the invariance.
