How can I hide a selection variant on a product page without hiding all variants?

[CasaMeroth]

I added a new variant in my products called "material" because I want to insert it as a filter through AI Search & Product Filtern, but when I create this filter it is also automatically inserted in the page of each product. How can I hide the material variant without deleting it, so that only the "letter" variant remains as shown in the picture?

if I remove the material variant, the filter you see in the following image is removed and I want it to remain:

Is there any kind of code or trick that can help me? Thank you for your help!