  Low temperature ($\sim$ 20~K) electron irradiation with 2.5 MeV relativistic
electrons was used to study the effect of controlled non-magnetic disorder on
the normal and superconducting properties of the type-II Dirac semimetal
PdTe$_2$. We report measurements of longitudinal and Hall resistivity, thermal
conductivity and London penetration depth using tunnel-diode resonator
technique for various irradiation doses. The normal state electrical
resistivity follows Matthiessen rule with an increase of the residual
resistivity at a rate of $\sim$0.77$ \mu
\Omega$cm/$(\textrm{C}/\textrm{cm}^2)$. London penetration depth and thermal
conductivity results show that the superconducting state remains fully gapped.
The superconducting transition temperature is suppressed at a non-zero rate
that is about sixteen times slower than described by the Abrikosov-Gor'kov
dependence, applicable to magnetic impurity scattering in isotropic,
single-band $s$-wave superconductors. To gain information about the gap
structure and symmetry of the pairing state, we perform a detailed analysis of
these experimental results based on insight from a generalized Anderson theorem
for multi-band superconductors. This imposes quantitative constraints on the
gap anisotropies for each of the possible pairing candidate states. We conclude
that the most likely pairing candidate is an unconventional $A_{1g}^{+-}$
state. While we cannot exclude the conventional $A_{1g}^{++}$ and the triplet
$A_{1u}$, we demonstrate that these states require additional assumptions about
the orbital structure of the disorder potential to be consistent with our
experimental results, e.g., a ratio of inter- to intra-band scattering for the
singlet state significantly larger than one. Due to the generality of our
theoretical framework, we think that it will also be useful for irradiation
studies in other spin-orbit-coupled multi-orbital systems.
