have the team come up with a list of achievable meaningful milestones (eg. 'eliminate use of nasty obsolete library X'), ensure some time is spared to progress them; it'll become clear if the team is net paying off or accruing
also, find someone who thrives on eliminating crap and let them get stuck in
Also make sure that person's work is recognized as being important.
I really like to eliminate crap, but I also try to avoid doing it as much as possible because it's something that never earns any recognition or praise. Historically I've had to really push to even get my boss to recognize it as an accomplishment during my quarterly reviews. Maybe management says they don't like technical debt, but that doesn't mean anything if incentive structures are designed in ways that encourage me to pile it on ever higher.
also, find someone who thrives on eliminating crap and let them get stuck in