The Gods are a logical and rational beings. If the offerings are edible or especially of an animal, they wouldn't want it to be disposed off but instead shared and eaten with anyone you can.
Pagan cultures are being infiltrated from ages, these misconceptions such as "killing an animal to offer it to the Gods and dispose it off" in other words "Sacrifice" were injected by the enemy into the weaker societies, even by greys themselves.
Our Gods love animals, I am certain they don't want an animal's death to go in vain especially in their name, they would want it to fill someone's belly rather than rot in the ground. Our Gods do not feed on Death energy. They forbid such practices. If one wants to offer something edible, just cook the food, keep it next to Father Satan's sigil or any Demon's sigil in your temple/astral temple, pray for it to be blessed, and consume it somewhere else after a few minutes.
But imo, an SS does not have to do all this, we are capable of doing something better. Instead you can offer them energy. One can do a thanks giving ritual, a Demon ritual, or simply vibrate their names with positive mood/intentions and send them energy.
If for centuries a large group of people who keep believing that a certain offering blesses them with goodness, safety, health, and etc from the Gods, then it certainly has an affect on the offering/gift. Beliefs are basically concrete thoughts that are much closely connected to the soul either temporarily or permanently, these have more energy than the everyday thoughts that come and go, a belief has more power to manifest something. It's why Abrahamism works on hijacking a person's or a group's beliefs.