Bones or shells remaining after eating, are Mukse. If so, how can they be removed from the table? Hacham Bension (Or Lesion 26:7) offers three solutions. One option is if they pile up to the extent that they become "Ma'us" (disgusting), they are designated "Graf Shel Re'i"-a putrid item, and the Halacha permits moving them in a normal fashion. However, not every case meets this classification. It must be a considerable amount of bones to make it truly repulsive.
A second option is to use the back of the hand to brush them off. This is referred to as "Tiltul K'Lahar Yad."
A third option is to take a knife and brush them off. This is called "Tiltul Min Ha'sad"-moving Mukse indirectly. This solution applies only if the space on the table is needed for another purpose.
If the bones are edible to animals, they are not Mukse. For example, chicken bones are edible to dogs. Even if he personally does not own a dog, but there are dogs in the city, it is permitted. Hacham Bension rules that the dogs must be within walking distance, whereas Hacham Ovadia is lenient even if the dogs are at the far end of the city. However, egg shells, olive pits and nut shells are not edible to animals and can only be moved utilizing one of these three options.
Bones and shells that are inedible are Mukse and may be removed from the table only if they become putrid, or with the back of the hand or using a knife (if space is required on the table). If the bones are edible to dogs, they are not Mukse, even if the dogs are not immediately at hand.