Could you help me understand this sentence: "After correcting for this age bias as a function of redshift, the SN data set aligns more closely with the cold dark matter (CDM) model”?
The CDM model has no dark energy, unlike the LCDM model. The L stands for Lambda, which is the dark energy term in the Einstein equations. So they are saying when accounting for this effect, our universe looks more like a universe without dark energy, at least when only considering the supernovae probe.
That's only if you consider the supernovae data alone. In combination with other probes like BAO, etc, the combined data are pointing to a Universe with a dynamical (or time varying) dark energy model.