The Cambridge Grammar of the English Language, page 148, reads
I would like to have met her and I would have liked to have met her, which are often used to convey the same meaning as I would have liked to meet her, are ambiguous: they also have interpretations in which anteriority applies to the meeting. These interpretations are pragmatically unlikely in the examples chosen, but become more salient if we change met her to finished it.
What are the two interpretations of such sentences which make them ambiguous?