Charter won't let me delete emails

I'm helping a little old lady who has Charter email on her two-year old iMac. Her inbox has over 5,000 emails in it. I deleted most of them, and a few minutes later, her network connection showed lots of incoming data, and the 5,000 emails were restored. Apparently Charter insists upon acting as a backup for her email and refuses to let any of it be deleted. I don't think that iCloud is restoring the old emails, as her Preferences settings for iCloud do NOT have Mac Mail checked for backup. I don't have Charter email so I'm not familiar with this problem.

I assume that I'll have to log onto her Charter account and alter some setting to fix this problem. Can anybody give me some orientation advice on how to proceed? I can't log onto her email account from my machine, and I don't want to engage in random exploration of the huge Charter website from her home.