Hype has never had specific options for controlling the output of GIFs beyond what is found in the current export dialog.
GIFs, with their highly limited color palette and single transparency bit are hard to make look right in a general way. Software like ImageMagick (which Hype v3.6+ uses under-the-hood) have a plethora of their own options that can be configured. Setting these up is really more of an art than a science based on the content of your GIF. If you need a high degree of configurability, you can probably instead export as a PNG Sequence and then use other software to determine the best settings.
That said, in Hype 3.5 and prior, Hype used Apple’s GIF export instead of ImageMagick’s. Overall we found the ImageMagick engine typically produces better results and lower sizes, but this is content dependent and not always the case. If you want to see what Apple’s engine can provide, there is a hidden preference that can be activated in the terminal:
defaults write com.tumult.Hype4 AnimatedGIFEngine Apple
To change back to the default, use this command:
defaults delete com.tumult.Hype4 AnimatedGIFEngine