Tested it out:
Created new save.
Went immediately to manage world and opened the Mayor Whiskers and Captain Whitaker households
Their households were reset upon opening them with sims with no names, aspirations etc.
Exited these households by cancel.
Opened Sienna and Gooseman households, they were there without the horses.
Opened Lynx household, no cats.
Looked at the map for all 3, none were shown with their pets.
Checked the Grove family, which I didn't open, and on the map icon they were already without pets.
Upon reopening the game, both Mayor Whiskers and Captain Whitaker households were gone.
So it looks like you don't need to save to trigger this and the game already don't have them, despite the thumbnails showing them in the other household category.
