Although my question is specific to IT industry, I think it can be generalized to a question about dealing with something that was done poorly by your predecessors.
I joined my current team some time ago, and at that time there was already a pretty large codebase in the project. Parts of the codebase are written in a poor fashion, and we're constantly experiencing problems with that functionality. The development team has already brought this problem to the attention of the management and there are plans to review those parts of the codebase and potentially reimplement the functionality from scratch. However, these tasks have very low priority on the backlog, and given the size of the team and the workload, probably "never" is a pretty close time estimate for that work being done. At the same time, we receive bad reviews from the customers and stakeholders about poor user experience. Is there anything else the development team can do to convince management that this is high priority job?