The phrase "back scratched" is a common idiom used to describe someone who has received help or a favor from another person. There are several synonyms that can be used to replace this phrase, depending on the context and the specific meaning intended. For example, "indebted" is a synonym that can be used to describe someone who owes a debt of gratitude to another. "Favored" is another synonym that can be used to describe someone who has been shown kindness or support. "Assisted" is a more general synonym that can be used to describe any type of help or support given to someone.