I finally figured out how to delete competed reminders on iOS.
You can create a shortcut to do this task. It took me a while to figure it out. In Shortcuts, you have to select what you want to act upon, and then act upon it in another step.
First, when you create a shortcut, you add an action. Go to Apps, look for Reminders, and then select Find Reminders. You add a filter in that step. One of the things that confused me is when I clicked on the filter, it showed me only List is and the name of a list. It took me a while to realize you can click on List is to change the filter. Change the filter to Is completed.
Now add a second step. If you need to, Select Apps and Reminders again. Now select Remove Reminders.
That’s it. Selecting this shortcut will remove deleted reminders. I had over 15,000 completed reminders and it took about ten minutes to run. If you leave Shortcuts before it finishes, the reminders don’t delete. After the first delete, it now runs in under a minute.
You can add an automation and have it run on a regular basis.