You may find some resources on
romhacking.net that might help you out a bit. Also
SMW Central may have some communities that focus on Mario Kart.
Otherwise, break out the debugger and get to work.
EDIT: looking through the latter forum, I found
this. If I interpreted this correctly, what you have is title screen graphics that use some form of compression. What this means is you would need to find out how the compression works, take your hacked title screen, compress it, and hope that it fits within the bounds of the original graphic. This requires extensive knowledge of 65c816 assembly, intimate knowledge of the SNES 4bbp tile format, and a lot of time debugging. If this is your first foray into ROM hacking, I would try something simpler.
Another edit: okay, after looking at
this, it appears that Lunar Compress can do all the gruntwork for you, you just need to supply it the ROM and offset. Not too terribly hard.