Representatives for the Recording Academy didn't immediately respond to email and phone messages requesting comment.
Ehrlich told Billboard that he was taken aback by the family's complaints and said he believed the tribute was appropriate.
Cole said she doesn't want to take away from the other musicians who were given tributes that night, including BB King, Glenn Frey and David Bowie.
But she said there was no dialogue mentioning her sister's four-decade career that earned her nine Grammy Awards, and the tribute felt like "an afterthought."
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"There were major tributes and major acknowledgements that were done and our sister was basically shoved into a cluster of artists at the end on a small screen," Cole said.
Cole said she had hoped that the Recording Academy would find an artist to perform her songs in her honour.
- AAP