In the context of the issue that doesn't really make sense. The issue is that the home office think you left and didn't come back. How would an exit check tell the home office you have come back into the country?

In a country that has exit checks, in order to go airside, a border agent will stamp you out and record your exit. If you were to get stamped out and then decide that you don't want to catch your flight after all, you'd have to get stamped back in again (often not a real stamp these days).

In the UK there's no exit checks. The only information they have is that you booked a flight. This is "Advance Passenger Information" which all airlines are legally required to submit. They don't know if you've actually boarded the flight, they just assume that if you booked a flight that it means you left the country.

The exit check doesn't tell them that you've come back, they know that already unless you cross the land border. But it does tell them that you truly left and stop the guesswork.