延滞料 means a fee charged when something is returned or paid late, such as a library book or loan. It is an unusual and memorable word to encounter in a love song.
In this song, 愛の延滞料 means the emotional "late fees" that keep piling up as the characters delay dealing with their relationship. The rental and borrowing imagery turns unresolved feelings into a clever financial metaphor.
The title "愛のレンタル" means "Love Rental", and Macaroni Empitsu runs with that idea all the way through. Love here is something you borrow and owe on. There is "たぶん続く愛の貸し借り" (the lending and borrowing of love will probably go on), and later the best joke in the song: "どんどん積もる愛の延滞料ダ" (the late fees on love keep piling up). That is the language of a video rental shop, applied to a relationship where nobody is returning what they took.
The singer wants more than he gets. He sings "甘えてほしいのに" (even though I want you to lean on me) and "大袈裟に欲しがってほしいのに" (even though I want you to want me, over the top), then asks "いつから僕たちは" (since when have we) "交われないことになったのかな" (ended up unable to cross paths?). His answer to every problem is a little silly and a little sweet: "ずっと僕と踊ればいい" (you should just keep dancing with me). Look out for the wordplay in "憂いのでんでん虫かよ" (are you a gloomy snail or what?) next to "電話もぜんぜん無視かよ" (you're ignoring my calls too?). "でんでん虫" is a cute word for a snail, picked mostly because it rhymes with "ぜんぜん無視" (totally ignoring), and the "かよ" ending is a casual, eye-rolling "seriously?". There is also a nice aside where he admits "たまにはママに会いたい" (sometimes I want to see my mom).
Macaroni Empitsu (マカロニえんぴつ) is a Japanese rock band that came together in 2012 at Senzoku Gakuen College of Music, built around singer and guitarist Hattori. The current line-up is Hattori, Kenya Takano on bass, Yoshiaki Tanabe on guitar and Daiki Hasegawa on keyboards. Fans call them Makaen for short.
They spent years playing live houses around Tokyo and Yokohama and releasing mini albums on indie labels before making their major-label debut with Toy's Factory in 2020. In 2021 they won Best New Artist at the 63rd Japan Record Awards, and their song なんでもないよ、 (Nothing's wrong) later became their first track to pass 600 million streams on Oricon's streaming chart.