Koshering coffee cups for pesach

If I have glazed ceramic coffee cups (the kind you might get in a restaurant) that have only been used for tea, coffee, milk, sugar and splenda, do I have to pack them away for pesach. The cups have been drunk while eating chametz, like a cookie or cracker, on ocassion. I imagine the cups have the status of kli sheni because hot water is poured directly from a hot water dispenser. In the past, because of doubt, I just packed them away. But, it may not be necessary. I don’t know if washing in the sanitary hot cycle of the dishwater would have been enough, or if i have to do hagala. Thank you.

Keli sheni
Just clean well