The fake "songs of Bilitis" were invented by the French poet Pierre Louÿs in 1894. Louÿs presented his work as a collection of poems "translated for the first time" from original Greek texts inscribed onto the walls of Bilitis' tomb, but these texts do not exist. Louÿs refers only to a fictional German publication in which the supposed excavator of the tomb gathered the poems.
The fake poems seem to have fooled some scholars at the time, given that Louÿs clearly did his homework and freely cited from real ancient works. Louÿs' volume was translated into several languages - but this may have been mainly for its value as a work of erotic poetry, which was his specialty, and for his supportive treatment of the topic of female homosexuality. Leading experts of Greek history were not convinced, and anyone who made any effort to trace the source would immediately discover that the whole thing was a hoax. Louÿs' friend allegedly admitted as early as 1898 that they had come up with the songs of Bilitis together in an attempt to expose the arrogance of ancient historians.
These days the episode seems to have been completely forgotten; to my knowledge, nobody believes the songs of Bilitis to be genuine, if they have heard of them at all. Greek scholarship was unaffected by the hoax. Its effect was greater in literature and art (most directly because Debussy, who was a close friend of Louÿs, set several of the poems to music).
The source for this post is a short article on the hoax by R.A. Pack, 'Two Classical Forgeries', American Journal of Philology 110.3 (1989), 479-483.