Are you sure there isn't something there to create that border?
What is that you are exporting? Does it have a background?
Is it vector? Can you select it and all of its parts individually while checking the Appearance Panel to make sure there aren't any borders / outlines?
Can you show the gif to us?
2013 Intel MacPro
3.5 GHz 6-Core Intel Xeon E5
64 GB 1866 MHz DDR3 ECC
AMD FirePro D500 3072 MB
Software OS X 10.14.3