In Japanland, records are sometimes called donut discs/plates/records/etc.
The joke that Mami thought Chihaya brought donuts didn't seem to translate to English very well, but there is an LP called Donuts by J Dilla, so some changes were made.
It's got a few neat songs, I could see Chihaya appreciating some of them.
https://www.youtube.com/watch?v=jMu47CsLm0M