Hi Is it permissible to allow an animal such as a cat or dog onto a table where food is being consumed and to allow the cat or dog to eat leftover food from a human’s plate after they have finished their food? Thank you

ב"ה Shalom, The Rema in Shulchan Aruch (167:5) states that a table is like the Mizbe'ach=Altar of the Bet Mikdash. From here, many Rabbis inferred that a table is a place which is to be treated with respect, not to sit on it, not to crush bugs on it or to do any other repulsive act. This is especially so with a table with food on it. ( Additional Halachot apply , if the table has Torah books on it). According to this, it would be improper to have an animal on the table, especially when food is on the table. It is also common among pet owners to have their pets behave with "table manners" while the pet owner and guests are eating. (For references see : (שולחן ערוך רמ”א סי’ קס”ז סעיף ה’, ערוך השולחן סי' קפז: יב, פסקי תשובות אורח חיים סימן קסז אות ו , רבבות אפרים חלק ג’ סי’ תפו, רבבות אפרים חלק ו’ סי’ צ”ה All the Best