[Baertram]

Afaik you can only manually edit the SavedVariables\AddonName.lua file (where AddonName is the addon's name like e.g. JoviexAddonSettingsTransfer.lua) and search for the old toon names.

Then remove the complete table starting with ["character name here"] = {
...}
And the settings should be gone.

If the settings are not stored by the name but the unique ID, something like ["8012232132313"] = { ... } you might not be able to see which ID is the ID of an old char.

You can use this function ingame to check your current characters and their unique IDs (will be printed to the chat) to compare them with the ones in the savedvars and strip those not found:

--Get your characters/toons and their unique ID
function getYourCharData()
    --Check all the characters of the account
    d("[getYourCharData] Your character name = uniqueIds are:")
    for i = 1, GetNumCharacters() do
        local name, _, _, _, _, _, characterId = GetCharacterInfo(i)
        local charName = zo_strformat(SI_UNIT_NAME, name)
        d(">" .. tostring(charName) .. " = " ..tostring(characterId))
    end
end

Put this function somewhere in any of your addon's EVENT_ADD_ON_LOADED function and do a /reloadui.
Afterwards you should be able to type in the chat:

/script getYourCharData()