This is a good approach for lots of things…. Dad always used to say this for jobs, cars, etc….
I’ve been in management for 20 years. Over this time I’ve been fortunate to lead many teams and the vast majority of folks were long tenured and either developed with me and accepted a promotion from within or retired. I’ve had a small handful that've left, and all but one would be welcome back. The one person was talented and took an internal promotion and just wasn’t a great fit for the team.
Since it was only a week, and assuming they left on good terms, I would sit the person down and have a very short conversation about the terms of re-employment. For example, they’re not getting a raise for leaving for more money and then coming back. If HR policy provided for it, I would try to get any seniority/tenure related PTO or other benefits restored, but compensation would resume at the prior amount. In addition, the next increase would follow new-hire guidelines, not the regular schedule. People have to understand there are consequences for their actions.
I would be very firm on the compensation point. In my experience people don’t leave a job they like over a few dollars. They leave their boss or team for a variety of reasons. As a manager, if I’m doing my part, I hire the right people first and then mentor them and treat them the way I want to be treated. If this isn’t enough, then they’re happy to leave and see what else is out there. This is the same reason I never make a counter offer if somebody says they’re leaving.