Based on your question, I'm guessing you're asking about Snagit on Windows or Mac.
Did you download the Snagit trial from the TechSmith website (techsmith.com)? If you did, I'm guessing that you had already been infected by malware before installing Snagit.
The signin screen is a web browser inside of the application, and if you're on Windows it's essentially loading our account site through Internet Explorer. I'm guessing that something has already infected your Internet Explorer and when it opens you're triggering the malware.
I would also guess that if you don't have Snagit open at all, and launch Internet Explorer on your computer you'd get similar results.