In light of the cultural objection to criticizing the dead, most people find a way to deliver
a left-handed compliment:
Praise that is subtle dispraise; reluctant and dubious praise:
Telling that amusing story of his drunken tomfoolery was a left-handed complement.
Depending on the severity of the criticism and nature of the objections other labels may fit:
[MASS NOUN] formal
1.0 Criticism or censure:
Her animadversion against her dead father was understandable even if it was awkward.
An attack on the reputation or integrity of someone or something:
It is generally considered rude to cast aspersions on the dead while everyone is mourning deeply.
1.0 Harsh criticism or censure:
His evil deeds earned Hitler almost universal opprobrium.
Because it only benefits the critic, many people would consider public criticism of the dead cavil until some time of mourning has passed:
A petty or unnecessary objection.
All the cavil is water under the bridge.