Does tea keep mosquitoes away

Yes, it actually does.
You will not find any mosquitoes around a field growing tea. The smell of tea repels them.

You can drink tea to act as a repellent as the tea will be present in your sweat, repelling mosquitoes. You can also dampen some tea and leave it near doors and Windows to keep them away. Though it might be strange to the neighbours seeing teabags hanging from your doors on string.