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In a smart grid environment some customers employ third-party meters and terminals for integrity verification of the smart meter power measurements reported by the electric utility company. We address the security issues that may arise under the presence of a third-party wireless terminal. In this paper we consider a rate-distortion perspective that contrasts the Slepian-Wolf distortionless coding approach recently presented by Varodayan and Gao  for integrity verification through redundant metering. We show that through the use of a limited secret key, we can impose a certain minimum distortion on the eavesdropper, while enabling the wireless terminal to retrieve the measurements losslessly with high probability. We highlight the advantages of our approach.