  Problems with the concordance cosmology $\Lambda$CDM as the cosmological
constant problem, coincidence problems and Hubble tension has led to many
proposed alternatives, as the $\Lambda(t)$CDM, where the now called $\Lambda$
cosmological term is allowed to vary due to an interaction with pressureless
matter. Here, we analyze one class of these proposals, namely,
$\Lambda=\alpha'a^{-2}+\beta H^2+\lambda_*$, based on dimensional arguments.
Using SNe Ia, cosmic chronometers data plus constraints on $H_0$ from SH0ES and
Planck satellite, we constrain the free parameters of this class of models. By
using the Planck prior over $H_0$, we conclude that the $\lambda_*$ term can
not be discarded by this analysis, thereby disfavouring models only with the
time-variable terms. The SH0ES prior over $H_0$ has an weak evidence in this
direction. The subclasses of models with $\alpha'=0$ and with $\beta=0$ can not
be discarded by this analysis. Finally, by using distance priors from CMB, the
$\Lambda$ time-dependence was quite restricted.
