How to prevent a vinegar taste when poaching eggs (using vinegared water)
I assume you mean eggs that have been poached in water with vinegar added?

I usually add vinegar to my poaching water when making poached eggs. However, I rarely taste the vinegar. I would suggest


Use less vinegar. I use no more than a tablespoon for a shallow frying pan's worth of water
Use a milder vinegar like white wine vinegar, or even lemon juice
Use really fresh eggs if you can, in which case you don't even need vinegar


Lots of people use a saucepan full of water to poach eggs. I used to, but always with inconsistent results. Usually the egg white would just disintegrate and form a foam.

Now I use a small, shallow frying pan. This means the egg white has less opportunity to disintegrate, and also means I need to use less vinegar to help the white set.

If rather than poaching you mean pickling, there's little you can do to remove the vinegar taste, as the vinegar will have penetrated the egg thoroughly.