See my other answer below: trying to convince the payers that there are extra costs due to "technical debt" accumulated somehow during the lifetime of a sw project would sound "unconvincing" because from the point of view of the business that would be part of the job of the same people that are now asking more money/time/resources to fix it.
This reads like it's in a vacume and assumes the business requirements were comunicated, they were clear, and and static. None of which is reality. Additionally things get updadated and need con rant maintenance. Gone are the days of writing code and letting it run untouched for years.
Tech debt usually occurs when the people implementing it aren't aligned with the with the stakeholders.