What can one use to balance/neutralize too much black pepper in a (pea-)soup?

You might have to make a second batch of soup and mix it in. (Note: Do not pepper the second batch.)

I’ve read that you can add a little lemon juice to neutralize the pepper. That and/or a slice of bread to pick up excess pepper.

Milk products can counteract that kind of pepper heat. Drop a dollop of sour cream into the bowl and take some of the cream with each bite, or take a sip of milk between bites of spicy soup.

Yogurt will remove the heat of the pepper

I would do what @marinelife suggested, just make another tin, and store in the fridge the leftovers. It will keep for a week. However, what @Blueroses suggested should work as well, a little milk, cream, sour cream, or even a pat of butter, whichever you prefer, will cut the pepper a little.

what about chicken or veggie stock, it will thin it out.

Cooking pieces of peeled potato in the soup will help absorb too much salt. Would that work with pepper too? The potato will add texture to the soup, but you can mash it. The potato and peas will taste good together.

I would use some sour cream or some cream cheese :)

Thank you all for your advice!
I will not use them as I am planning to be more careful with the pepper the next time (if, for whatever reason I do mess it up again I will try them) :-)