Speaking as a security consultant - don't give a reward. What they did is technically illegal and not in the spirit of security testing.
If someone finds a vulnerability accidentally (I've done this before), they won't ask for a reward if they are professional and the company has no bug bounty. It's reasonable to tell a company out of respect - it's unreasonable to ask for payment, that implies almost a ransom and will encourage more of it.
There is a problem with bug bounties these days in that they attract a lot of people desperate to get into the InfoSec industry who don't necessarily know what they're doing and have no professionalism (see @CluelessSec for example.) Don't encourage it by giving a reward.
Cold calling (or emailing) companies to solicit penetration testing is okay, casing the company for vulnerabilities and asking for payment is not. I do suggest you find someone to do a solid penetration test of your company however just out of principle.