General Information - How to Dispose of Offerings
Let me start by saying that there is no one correct way to dispose of offerings. Different people on different paths dispose of them in different ways. A large part of it has to do with accessibility for certain disposal methods.
In the vast majority of cases, it is appropriate and acceptable to dispose of your offering once it has been received. Some practitioners say that they wait for a certain feeling that they get, for some it's an energetic signature, for others it's an emotional feeling, and they will take that feeling as an indication that the energy from the offering has been consumed by the entity they are offering it to. Other practitioners leave it for a certain amount of time, usually an amount of days that corresponds numerologically with the desired outcome, especially if they're offering is one of reciprocity. Still others will leave it for an amount of days that corresponds numerologically with that entity, if there is such a correspondence.
Some practitioners will leave it until it gets old, it starts to shrivel, or mold starts sprouting, at least if it is organic or something that deteriorates. They will consider that to be an indicator that it has been consumed. There are some cases in which an offering will sit on an altar for an extended period of time because it does not shrivel, mold, or decay at a normal rate. Many practitioners who have this happen consider it to be a sign that their entity is enjoying it for a prolonged period of time. I have even seen some practitioners keep things like apples and other food stuff on their altar for months at a time, just waiting for it to show signs of decay. Many of these practitioners consider the extended decay times to correlate with how much the entity likes that offering; the longer it takes to decay, the more they like it.
If the offering is being left out for a short period of time and it is consumable, it is normal for some practitioners to consume it as a form of disposal. Modernly, this is usually part of a waste not mentality. In Kemeticism, modern practitioners mirror what ancient practitioners did, taking the consumable offering after it is believed the essence has been consumed by the entity, and then passing the offering around the priests and temple staff, or simply to the practitioner and maybe their family in modern times, as a blessed and sacred meal. In Hellenic polytheism, it is also common for the practitioner to consume the offerings as a shared meal with the Gods, though not all Hellenists follow this. The Gods were thought to consume the parts people couldn't eat, bones, fat, aroma, etc; and the people ate the rest. In Nordic Polytheism, it was also normal to eat the animal sacrifices after their blood was used to consecrate altars and people, the sacrificial meat would be shared in communal feasts to strengthen the bond between the community members.
All throughout antiquity, people by and large consumed edible offerings after they were offered to their entities. This was normal and expected. Many modern practitioners follow this route and will consume their offerings. For some reason that I haven't quite figured out yet, though, many modern practitioners refuse to consume their edible offerings because they feel it is disrespectful to the entity to 'take what belongs to the entity for themselves'.
Some consumable offerings, and some other offerings that are capable, are burned as a way to release their essence to the entity. Ancient Greece would burn animal sacrifices and some of their offerings, consumables, spells, etc. Ancient Egyptians primarily burned incense, not food. Consumables and other offerings were burned by ancient Nordic cultures, too. Some modern practitioners refuse to consume offerings as they see it as rude, greedy, or gluttonous, or stealing as it is taking what belongs to the entity.
Buried offerings were used frequently for offerings for the dead in ancient Hellenic, Kemetic, and Nordic Polytheism. They were also, less commonly, buried for deities across all three. In modern times, it is considered good form to bury offerings for Hekate and other cthonic deities, specifically at a crossroads.
Modern practitioners toss biodegradable offerings into moving water as a form of disposal. Ancient Greek practitioners would throw offerings in the rivers, the sea, or sacred springs. Ancient Egyptian practitioners disposed of libations sometimes by pouring them into the Nile. Ancient Norse cultures would dispose of some offerings in rivers, lakes, bogs, and other bodies of water.
Some practitioners only follow the consume, bury, burn methods of offering disposal, seeing those as the only respectful methods. Other practitioners, especially those who don't have access to land to bury things on, pits or safe places to burn things, or are offering non consumables, will instead throw the offerings away once they've been energetically spent.
This has actually caused discourse in the wider theistic witchcraft and pagan communities, as some people see throwing away the offerings once done to be highly disrespectful, equating that entity to no better than trash, and citing that ancient people did NOT throw away offerings into the trash due to their sacred, blessed nature.
Others defend the throw away method, saying that times have changed, access to certain methods of disposal simply aren't feasible for many modern, especially urban or city-based practitioners, and that once an offering has been used, if it's not something reusable like jewelry you wear on honor of that entity or to keep that entity close, that offering has no more use to the entity and is free to be disposed of as necessary. They cite that it isn't about respect or disrespect, it's about necessity, efficiency, and functionality. Especially for practitioners who are in the broom closet.