Ask if you can see the SMTP logs.
Changing those settings wouldn't matter unless you were sending bulk emails to a bunch of recipients at once. It would not prevent a single page that sends an email from being accessed more than 200 times per hour and initiating the block.
My best guess is that a hacker or spammer was trying to send a bunch of emails from your contact page using a bot and that caused the issue. However, I'd see if you can find out the cause definitively before working on a solution.
Try to get the logs to see what emails were being sent at what time intervals and once you know the page and content causing the issue we can work on a solution for you.
Some possible solutions include: Using authenticated emails with a different SMTP server which usually don't have caps, Add IP address check and logs and don't allow more than one email from the same IP address every 5 minutes, Adding CAPTCHA and/or random questions to the contact form to prevent bots from doing multiple submissions. There may be other options too, but these are some that can be considered.
