Nobody is using this or followed up on 2 or so times I've asked about it, so it's been removedBy request, you can now specify Tera Type: None in analyses. This functionality is intended for when you should not ever tera a Pokemon, similar to the "No Ability" ability or "No Item" item.
Right now, it doesn't do much, and will just result in no Tera Type line being shown on the Dex. But, it may do something different in the future, so if you all think this is useful please use it in your uploads so we can get a better idea of what to do.