The issue seems to be that TeamSpeak is using CloudFlare’s DDoS protection in place. See the screenshot at the bottom of the answer. More details on what this protection is/means on this official Amazon page on CloudFlare’s security features:
CloudFlare leverages the knowledge of a diverse community of websites
to power a new type of security service. Online threats range from
nuisances like comment spam and excessive bot crawling to malicious
attacks like SQL injection and denial of service (DOS) attacks.
CloudFlare provides security protection against all of these types of
threats and more to keep your website safe.
More specifics on their advanced DDoS protection methods can be found here:
CloudFlare's advanced DDoS protection, provisioned as a service at the
network edge, matches the sophistication and scale of such threats,
and can be used to mitigate DDoS attacks of all forms and sizes
including those that target the UDP and ICMP protocols, as well as
SYN/ACK, DNS amplification and Layer 7 attacks. This document explains
the anatomy of each attack method and how the CloudFlare network is
designed to protect your web presence from such threats.
Now how does this factor into the “503 Service Temporarily Unavailable” you are seeing? Well, that means that the site you are trying to access is under such a high level of protection from the Amazon CloudFlare DDoS detection/mitigation services that non-standard access via a command line tool like
curl is just not possible at this point.
FWIW, I have done a few different
curl attempts from the command line and I believe what happens is that CloudFlare’s DDoS protection just acts like a huge web page proxy for sites that opt to use it. And the “real” website exists somewhere other than the IP address the hostname resolves to. Sites like this claim to give you the “real” IP address connected to a CloudFlare hostname, but it doesn’t seem to work at all. Or maybe the IP address that is given is valid, but the way the service is setup just denies you direct access to the real site without jumping through CloudFlare’s loops.
Which simply means, the best you can do is sit and wait and maybe in a few hours or possibly days the security issues that site faced will fade away and standard
curl calls can be made. But the reality is if this security protection is in place, and is solid, and the website owner does not disable it, then you can’t do much to get around it.