How does this bank delete a sent SMS?

You send a second SMS with the same PID and it’ll overwrite the first one. It’s in the GSM standard and described on Wikipedia: https://en.wikipedia.org/wiki/GSM_03.40

This Belgian bank sends new pin codes by SMS. Phones delete them after 2 days. How is this achieved?

Not sure but they don't automatically delete any of my SMS (pin codes or not) here in the US