alternative to nested loops for large data set

[Gribouillis]

You could start by grouping the card sections by their card_id. There are several ways to do that, here is one

from operator import itemgetter
import itertools

dic = {int(key): list(group) for key, group in itertools.groupby(
            sorted(card_sections, key=itemgetter('card_id')), key=itemgetter('card_id')))}

card_names = []
for card_id, qty in owned_cards.items():
    for sections in dic.get(card_id, []):
        card_names.extend('{}#{}'.format(s['name'], qty) for s in sections)

Alternately you could use more_itertools.bucket() if you have this module. Also note that in Python, 20 != '20'