How to protect carpet in rented home?

Don't know if this is what you are after but you can usually buy cloth backed plastic by the metre on market stalls, I've used it before and it worked quite well and was fairly cheap. it can also be bought in The Range if you have one nearby.I even covered some fabric dining chair seats with it and it lasted for years.
Hope your stepdaughter and children settle in well to their new home.

I'll second your post, emmasnan. DD used it under GS's high chair, and later under his toddler chair until he learned to control his feeding. She bought it from Dunelm, but i've seen it in a number of places. It's also useful for playdoh, painting and other messy activities. Lasts ages.

I used a plastic tablecover when mine were at that stage. Cheap enough to throw away when no longer needed and easy to store when not in use.

Old shower curtains were our protection of choice. Or even new ones bought very cheaply in a market or Dunelm?

Cheap rugs? Used to get stuff like woven plastic......Dandycord??

I use the cloth backed plastic under GS highchair bought an offcut from John Lewis but have also seen it in the local market

Great ideas. Thank you so much for suggestions.

Shower curtains are good and washable. Very cheap ones can be bought from B & M if you have one near you.