People with gut cancer get their gut removed regularly, sometimes a big chunk of the guts. Do they lose their memories?

Maybe. There was a guy who induced aphantasia after a stem cell transplant and one of the hypothesis is the loss of gut bacteria via antibiotics. https://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC8143657/

I reversed a life-long case of Prosopagnosia after doing some n-of-1 experiments with replenishing my gut bacteria, so it seems plausible to me that losing intestines could impact this.

I also have a friend had her intestines removed due to Crohn's disease. She had an infection from the surgery that put her in a coma she woke up unable to picture things in her head. Hard to say what caused it.