Passing messages from AWS to company site

I am looking for a way to pass log events from AWS application to my company site.

The thing is that the AWS application is 100% firewalled from everything except only one IP address because it's encryption related service.

I just don't know what service I should use to do this. There's so many services so I do really have no idea what is it.

I think I'd just use simple message service, does this makes sense? The thing is there's plenty of events (let's say 1M per day), so I don't want big extra costs for this.

Sorry for the generic question, but I think it's quite concrete - "What is the most optimal way to pass event message from AWS when volume is approx 1M per day each 256 bytes on average?".

I'd like to connect to AWS service instead to any of the EC2 hosts...

On both sides I have tomcats with AWS-SDK.