I hate pickled eggs.
When I finish a jar of pickles (big jar from Costco), I “boil” up a batch of eggs in the steamer (30 minutes), cool & peel and put them in the pickle juice.
What you HAVE to do though, is always use clean sterile utensils when removing pickles to avoid contamination of the juice. Thoroughly boiling the pickle juice also might be a good idea before introducing the eggs into the brine.