There are many places across the web and Stack Overflow where one is discouraged from changing the priority of a ThreadPool thread or TPL Task
It's discouraged, specially if you're upping the priority, because it can affect the overall performance of your system.
Not to offer an overcomplicated answer, but in general, thread priority is a complex topic. For example, Windows has 2 related descriptors: thread priority and process priority. Both range from Idle, the lowest, to Time critical, the highest. When you start a new process, it's set to the default, the mid-range (a normal process priority with a normal thread priority).
Plus, thread priorities are relative, meaning that even setting a thread's priority to the highest in a busy system won't ensure that it will run in 'real-time'. DotNET offers no guarantees on this, neither does Windows. From that you can see why it's better to leave the threadpool alone, since, 99.9% of the time, it knows best :)
All that said, it's ok to lower a thread's priority if the task involves a long computation. This won't affect other processes.
Increasing priority, however, should only be done for tasks that need to react quickly, and have a short execution time, because this can negatively affect other processes.