Does sacrificing an animal at Eid al-Adha on behalf of deceased parents benefit them?

The Eid sacrifice benefits above all the person who offers it, because it shapes their own attitude. What truly helps the deceased is giving charity and helping those in need on their behalf, especially if they themselves did so during their lives.

When people do something good for the deceased, the idea behind it is that the reward of that deed reaches them. For that to happen, however, the deed itself must carry a reward, for example because it serves other people.

The Eid sacrifice is different. It recalls Abraham (as), who was ready to give even his beloved son to God, because that is how he understood his dreams. God accepted this readiness but freed him from the misunderstanding and gave him a ram to sacrifice instead. Whoever offers a sacrifice today is meant to awaken this spirit within themselves. The second verse above says that it is not flesh and blood that reach God but righteousness. So the sacrifice shapes the attitude of the one who offers it. It can no longer change the attitude of someone who has died.

Eid al-Adha is also a festival. One may eat of the meat oneself, share it with relatives and friends and give it to the poor. It is a shared joy. That too is not a service whose reward could be passed on to someone else.

Charity and help for those in need are different. Whoever helps the poor in the name of their deceased parents does something that pleases God, and may ask God to credit it to them. The first hadith above confirms this. It is especially meaningful if the parents themselves did good for others during their lives. Then one carries on what death interrupted and asks God to accept it on their behalf.