I never heard of the function
GAMEPAD_CHAT_SYSTEM, "remove"
nor KEYBOARD_CHAT_SYSTEM, nor the base ZO_ChatSystem does provide that function
So I'm not sure if your hook here ever works "normal".
btw: Better set a local up in front of deleteIcon please, or else you will overwrite other addon's using this variable already.
The name is not unique enough to eb global!
Or rename that to a more unique global variable like GamepadChatIconBegone
Question:
When exactly do you want the bubble to disappear?
Always: Then try my RedirectTexture hack!
Only after chat minimizes and there are no new messages, until new messages come in: Then use my SecurePostHook(GAMEPAD_CHAT_SYSTEM, "Minimize", function() idea.
If you do not want the chat bubble to reappear you need to disable the chat tab options for chat channels like NPC talk.
As gamepad mode does not provide that switch to keyboard mode, right click the most left chat tab, choose preferences and disable the chat channel for NPC talk e.g.
Then switch back to gamepad mode.
It should no longer show you and NPCs text in the chat then, and only messages from zone/say/yell etc. (the channels YOU have configured for that chat tab) will be shown in chat and should raise the bubble to reappear again (if not using the RedirectTexture hack which should it hide always), to show you there are new messages.