On past jobs/projects we (me and the team, if any) never really cared about technical debt nor had a process to take care of it.
On my current project, the only technical debt we (me and the project manager) care about is the one reported by our code inspection tool (SonarQube). I usually have a look at it when I have time (usually a bit before the end of a sprint) and try to fix as much as I can. That's a very small scale project so that works for us.
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