> Does the mathematical test in 3dLMEr, which produced the z values for my above mentioned group*time interaction effect, have a name?

group:time is the interaction between group and time. It assesses the difference of the slope (or marginal) effect for time between the two groups.

> Since you said chi-square results for group:time and z values for [-gltCode Int-Ctlr_over_Time
> 'Group : 1*Intervention -1*Control Time :'] are conceptually equivalent and it's possible to use
> either one, I decided to use the z values, because those also show the direction of the group*time effect.

Yes, it makes sense to use the Z-values because it contains the directionality information.

> What is the correct phrase to use for the z values?

It shows the statistical evidence/strength for the group difference for the slope effect of time. It would be better to show the magnitude of the group difference (the sub-brick right before the Z-values) for the slope effect of time (as UnderLay on the AFNI GUI).

Gang