Shrift is a very old word for the penance given by priests after a person made a confession. It later came to mean the confession itself, although even that is now outdated. I believe you can still be shriven, but haven’t attempted that myself.
When prisoners where sentenced to death (In Britain) they were permitted to confess their sins to a representative of the church, just before execution. They weren’t given much time, so it was just a short shrift.
Since then, the phrase has come to mean to swift dismissal or brush off. Sometimes the phrase is written short thrift, but that’s not correct. At least at the moment – as I think this post makes clear, words and their meanings can change. As it’s the whole phrase which has been repurposed, not just a single word, no alternative lengths of shrift are now available.
I looked into all this, because while doing the (hopefully) final rewrite of the fourth book in my Little Mallow cosy mystery series, I used the term. When Mike attempts to visit Ellie in hospital, outside visiting hours, he’s given short shrift by the nurses. I don’t recall ever writing the phrase before, so wanted to check I had it correct. And then I got distracted. Not for the first time!

By the way, if you don’t already know where Little Mallow is, you can find out in a special issue of the Little Mag, which is the village’s community newsletter. As well as directions, there are short stories and a cake recipe.