Yes pigeons do grieve.
They are highly intelligent birds who mate for life, they develop strong bonds with their partner and will display signs of distress if their mate or one of their chicks dies.
Pigeons Emotional Intelligence
Pigeons are at the top when it comes to animal intelligence.
Testing has proven that they are self-aware and can recognize themselves, which in humans means that people can think about themselves and their environment.
Along with that comes a whole bunch of what we see as normal emotions, one of which is grief, the sense of loss.
Studies Into Animal Grief
Some scientists involved in avian studies believe that birds of all kinds can feel grief, but the only way to tell is through their behavior after a death.
Observers point out the altered behaviour among mothers or survivors of mating pairs in other types of avians, such as ducks, swans, crows, and penguins.
The birds poke or pull at the deceased, crying out, like they are vocalising their sadness.
Others may join him or her in what looks like emotional support and sympathy.
Skeptical observers claim that this behavior is only confusion, that they don’t really understand the concepts of death and loss.
There are other reported cases where one of the pair dies and the surviving bird commits suicide.
Conclusion
That pigeons mate for life suggests an emotional bonding or connection among pigeons.
It suggests that if one were to die, the other would feel grief.
This also applies in the case of one of their chicks dying. While none of this can be proven one way or another scientifically there is plenty of anecdotal evidence to suggest that pigeons do grieve.