Curious About These Ink-Stamp Marks In Old Stamp Notebooks

Got this stamp collection from my grandpa that he got during WWII.
I'm curious what these ink-stamps moght mean or signify. They're frequently in spots where stamps have been removed (sold or traded?).

These are pages from a stamp club "Circuit Book"
The pages are circulated from member to member, when you see a stamp you want, remove it, and place your initialled stamp in the space.

Your stamp prices are then tallied and you pay the total cost.

I buy these pages regularly, good source of stamps at good prices.

If the price is not shown in the square, then the page header may say
"This page all stamps 20c" etc

PS: One of the benefits of joining a club (It's great fun)

Thank you for the quick response!!