This is a catch 22 - but as it is an initial filter, then when paging the same thing happens as with eventual "marked/checked" records - it is a new page-load.
If it is a table with not too many records, you could maybe use the fantastic "scroll" suggested by pböttcher :
https://forums.appgini.com/phpbb/viewto ... f=4&t=2673
You could have the scrolling for 50-100 records and still have the paging. But the problem with paging will still be there.
Another way is to make a view in a "parallel" table that is filtered. But then the initial filtering will be there always. You can still filter, but it will be in the filtered table.
The normal unfiltered table will still be available, so you could have two tables shown - one with the pre-defined filtering and the other without. You still only have to maintain one table.
If the static filter is not an option, then I think you need some code that can check if you are on page 1 or not, and then only let the filter be active on page 1. This will also mean that when paging back to page one, the filter will be active again.
I cannot help with such eventual code.