reach, arrive, report, notify, forward
屆 centers on the idea of something reaching a destination or a person: arriving, delivering a report or notification, or forwarding something onward.
屆 is the traditional form of 届. It combines 尸 (a person) with 凷, which likely contributed the sound and the idea of reaching or arriving. The modern Japanese simplified form 届 replaces the inner component with 由.
The outer 尸 looks like a person bending forward to receive something, and the inner 凷 resembles a block of earth or a container being handed over. Together they suggest a person receiving a delivery or a message that has arrived.
For カイ, imagine a delivery person arriving and calling out 'Hi!' as they hand over the package: 'Hi' -> カイ, and the message reaches you.