You can't and you don't need to. Normally if these websites are actually storing your credit card info they are required to be PCI-DSS compliant. If they are not, then it's up to the credit card companies to prosecute them.
Now you might be wondering what in the event someone hacks their database, steals my info and uses it to commit fraud?. Simple You are insured against fraud by your credit card.
All cards with MasterCard Visa logos covered by fraud policies that will not hold you liable for fraudulent transactions if a charge is made through their system. There are however some exceptions you need to take into account as you need to comply to the following ruleset:
- Your account is in good standing.
- You have exercised reasonable care in safeguarding your card.
- You have not reported two or more unauthorized events in the past 12
- You do not have a commercial (corporate) card
- Fraud was done by an ATM transaction
And just another golden tip if you don't trust the website, don't give it your credit card details.
Now without knowing or being able to assess the backend system, there is no sure way of saying how these transactions are performed by Charity Water. It could be that they use a backend system which is either PCI compliant or does not store the card details and just passes them on to a payment gateway without you knowing.