Is the supplication and raising of hands after finishing a meal and before departing among the newly invented innovations (bid'ah)? And what should one do when facing such a situation?

Praying for one who feeds you is a Prophetic Sunnah (definition), as indicated by the Hadith (definition) of Anas, may Allah be pleased with him, that the Prophet, peace and blessings be upon him, prayed for Sa'd ibn 'Ubada when he ate at his house: "May the fasting break their fast with you, may the righteous eat your food, and may the angels invoke blessings upon you." As for guests praying for themselves and for Muslims, there is no harm in it as long as it is not mixed with innovation (bid'ah) or a forbidden act. However, one should not persist in it constantly lest it fall into the category of added innovation (bid'ah idafiyyah).