ChkMods will not delete the Spit MOD-folders if you have the checked 'Keep unknown mods'... But, as other files are being changed when installing the Griffion Spit(s), (one of 'm is the famous 'buttons' file, there are others), the Griffons will certainly not be available after running ChkMods and have it 'Fix Issues' currently, as ChkMods will change said files back to their original values.
You'll have to wait a bit, we're working on implementing the Griffon Spits.
When that's finished, you can run ChkMods again, and the result will be that ChkMods will install the Griffon Spits for you.
Unfortunately, I cannot tell when that will be...