What is the best word or phrase for, 'giving without expectation of receiving anything in return.'

Solution 1:

The term "charity" largely means what you're looking for, but again it's a noun rather verb.

There's "no strings attached"

Without conditions or restrictions, as in They give each of the children $10,000 a year with no strings attached. This expression dates from the mid-1900s, although string in the sense of “a limitation” has been used since the late 1800s.

https://www.dictionary.com/browse/no-strings-attached

The phrase "left hand doesn't know what the right is doing" has come to be used to refer to dysfunction, but originally it's from Matthew 6:3

But when thou doest alms, let not thy
left hand know what thy right hand doeth:

This is talking about giving to charity without feeling that you're owed anything due to it.