So the only way you’re going to get this resolved is to talk with WordPress and find out from them why your server is blocked in their firewall. Beyond that, there’s not a lot we can do.
There literally is no one to talk to at “WordPress”. This isn’t a company or anything like that. I’m pretty sure you’ve a network issue though on your host side.
Let’s try some CLI commands via ssh to get some info. First one is this to confirm what the Internet sees your requests as. This may seem redundant but give these a try to gather info.
Step 1
curl https://ifconfig.io/
Ideally that command will return one line, your external IP address of 69.16.221.200.
Next up, let’s rule out any DNS issues.
Step 2
dig api.www.remarpro.com
On my Linux box the IP address for api.www.remarpro.com I get is 198.143.164.251. I then use this openssl command to check that I can see the TLS certs from that server for api.www.remarpro.com.
Step 3
openssl s_client -connect 198.143.164.251:443 -servername api.www.remarpro.com </dev/null
Which should produce some output. On my server I see this at the top.
$ openssl s_client -connect 198.143.164.251:443 -servername api.www.remarpro.com </dev/null
CONNECTED(00000003)
depth=2 C = US, ST = Arizona, L = Scottsdale, O = "GoDaddy.com, Inc.", CN = Go Daddy Root Certificate Authority - G2
verify return:1
depth=1 C = US, ST = Arizona, L = Scottsdale, O = "GoDaddy.com, Inc.", OU = https://certs.godaddy.com/repository/, CN = Go Daddy Secure Certificate Authority - G2
verify return:1
depth=0 OU = Domain Control Validated, CN = *.www.remarpro.com
verify return:1
---
Certificate chain
0 s:OU = Domain Control Validated, CN = *.www.remarpro.com
i:C = US, ST = Arizona, L = Scottsdale, O = "GoDaddy.com, Inc.", OU = https://certs.godaddy.com/repository/, CN = Go Daddy Secure Certificate Authority - G2
1 s:C = US, ST = Arizona, L = Scottsdale, O = "GoDaddy.com, Inc.", OU = https://certs.godaddy.com/repository/, CN = Go Daddy Secure Certificate Authority - G2
i:C = US, ST = Arizona, L = Scottsdale, O = "GoDaddy.com, Inc.", CN = Go Daddy Root Certificate Authority - G2
2 s:C = US, ST = Arizona, L = Scottsdale, O = "GoDaddy.com, Inc.", CN = Go Daddy Root Certificate Authority - G2
i:C = US, O = "The Go Daddy Group, Inc.", OU = Go Daddy Class 2 Certification Authority
---
Server certificate
-----BEGIN CERTIFICATE-----
[ SNIP! ]
All that does is show me that my TLS handshake is working with that IP and servername.
When you do that, what do you get for steps 1, 2 and 3? What is your external IP and what do you resolve api.www.remarpro.com to? And do you see the TLS server for the api.www.remarpro.com server?