League of Legends (LoL) Question: How do you change core items to not show trinket?

Dunno if this is what you mean, but if you don't want the trinket to show in the build page, place trinket as the FIRST item like this:




You can change core items simply by checking the box in the 'purchase order' you want to be core.

Check the core items box for the build that you want to be the core items. To delete the trinket just don't add it to the items