Besides being a song by the 1910 Fruitgum Company it means the following (from Wikipedia)
Indian giver is an American English expression used to describe a person who gives a gift (literal or figurative) and later wants it back, or something equivalent in return. The term “Indian gift” was first noted in 1765 by Thomas Hutchinson] and “Indian giver” was first cited in John Russell Bartlettl’s Dictionary of Americanisms (1860)[as “Indian giver. When an Indian gives any thing, he expects to receive an equivalent, or to have his gift returned.” Thus it was really an exchange of gifts and not a matter of selfishness.
Nevertheless, the phrase can be considered offensive,particularly to American IndiansEtymology
It is unclear exactly how the expression came to be, but the consensus is that it is based on American Indians having a distinctly different sense of property ownership than those of European ancestry. One theory is that early European settlers in North America misinterpreted the aid and goods they received from local Indians as gifts, when in fact they were intended to be offered in trade. Many tribes operated economically by a form of barter system, or a gift economy where reciprocal giving was practiced.
Since the phrase was likely a cultural misunderstanding that unfortunately denigrates American Indians and no known English synonyms seem to exist, a group of freecyclers invented the new word “ersatzgiver” to replace it[ (ersatz means “substitute” or “replacement” in German.
This phrase came up when the discussion turned to ‘björntjänst’ in class. I have not yet found an equivalent in English but will keep looking.