Deseed is in some dictionaries. The usage examples I found were mainly using deseeded, and mainly in recipes. It is also quite often written with a hyphen.
Seeded can mean the same thing as deseeded - e.g. seeded raisins I would expect to have no seeds. But there is scope for some ambiguity with seeded, which is one reason for using deseeded.
From now on deseed, deseeded and deseeding will be accepted. I'm not convinced they should be common, so I'm making them rare.
I only found a few uses of the word deseeder, and they were mainly referring to a tool for deseeding pomegranates. (Whereas the usual reason for deseeding a fruit or vegetable is to discard the seeds, in the case of the pomegranate the aim is to use the seeds, and discard the fibrous matter surrounding them.) I find deseeder a bit too obscure for our list, even as a rare word.