Akeeba Backup does not modify your site when taking a backup. What you describe –and I confirm visiting your site– is certainly not the result of taking a backup of your site. So, let's try helping you :)
I think that you have simply configured a secret word in Admin Tools, jSecure or another security extension and this is what is performing the redirection. If you have reasons to believe it's Admin Tools (well, if you ask me, I think this may be it) please follow
the troubleshooting instructions to gain access to your site and go to Admin Tools, Web Application Firewall, Configure WAF. Take a look at the "Administrator secret URL parameter" option.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!