The CAS/TAS variation due to density error is much greater than the LSS change due to temp. variations.
So when descending in an Inversion layer the LSS in decreasing due to reduced temp and the TAS is also decreasing with CAS const. but the TAS reduction is at a much greater rate than the LSS because of the additional increase in density due to reducing temp. So if you kept CAS const. the TAS will reduce at a much greater rate than LSS and the Mno. will reduce. So to keep Mno. cont. the rate of reduction of TAS has to be reduced by increasing CAS.