If you're seeing 'manychat.com' in your bot's messages that contain Card or Gallery elements, it's not exactly Manychat branding that you're looking at. In fact, it's the link you've added to the message that has been shortened by Manychat's Card URL Shortener feature.
Card URL Shortener serves to collect CTR for your links - this can only be done if the link is run through our sever.
If you have Pro Manychat account, you can disable this feature and make your links appear as they are. To do this, go into Settings -> General -> find Card URL Shortener -> choose 'shortener is disabled'.
Don't forget: disabling Card URL Shortener means that Manychat won't be able to collect CTR data for your links.