The first thing to note is that the ICF is not unique in having the capability to take "foreign played" FIDE rated games into account in calculating national ratings.
Before the recent change by the ECF (English Chess Federation) to monthly Elo-style ratings you could if you wanted to write to the ECF grading officer and tell him about foreign played tournaments and request that they be included in your biannual ECF grading. With grading lists only updated once every 6 months this manual process was just about manageable by the moribund ECF which still struggles with 21st century computerization and the modern digital world.
With the new, monthly, rating system this appears to be a bit of a struggle for the ECF. This is what the ECF currently have to say on this:
With the introduction of monthly rating, the rating team are reviewing the arrangements for the rating of games played abroad. If you have an enquiry of this nature you can email the Manager of Rating, Brian Valentine, to find out how the process is progressing (see https://www.englishchess.org.uk/about/ecf-officials/)
With the Israeli Chess Federation, however, I don't need to tell them. They pick this information up automatically. This information is all available on the FIDE's rating website. It can be picked up programmatically by a sufficiently modern, automated chess federation.
Note that, as with all modern Elo-based rating systems, each individual game is rated individually. Games played under different rating systems are all given equal weight.
For an example of how low the FIDE rating of Israeli tournaments goes, here are the tournament details for rounds 3 and 4 of the B league in Tel Aviv for March (rated in April) 2022. The ratings of the players vary between 1062 and 1689.
Here is my FIDE playing record.
Here are the details of my last FIDE rated tournament giving all the details needed for rating calculation.
FIDE even has a record of the PGNs of my games played where the organizers have submitted games to FIDE.
All that is needed to access this information is my FIDE ID. Since most chess in Israel is both FIDE and national rated (the exceptions are usually weak junior tournaments for whom full FIDE rules, e.g. illegal moves losing the game, are not appropriate) the ICF have the FINs for all FIDE registered Israeli players. Automating the process is then a straightforward programming job.
Note that the ICF has no knowledge of my ECF rated games. Before the latest changes in ECF grading / rating the game information was not readily available. It is now. Here is the ECF's record of my last 3 months' ECF rated games. The one problem the ICF would have trying to incorporated this additional information is that they don't know how to interpret ECF ratings.