This is already generally being accounted for (assuming we have the correct cosmological model for the Universe). The CMB measurement is probing the Universe at an early state (when the Universe was ~380,000 years old) and the Hubble "constant", H(t=380,000 yr), was different at that point from what it is now, H_0 = H(t=13.7 billion years). The comparison to the current Hubble constant (e.g., determined from Cepheids) is made by evolving the CMB Hubble "constant" value to today, under the assumption of our best cosmological model model.
Of course, if we have the wrong cosmological model, then that could be a reason for the discrepancy, and that might point to "new physics". Alternately there may be some systematic in the Cepheid technique that is causing our H_0 estimate to be somewhat off.