There is a small ad at the top right of the header header. It is hidden on mobile. It is a block.
When logged in as admin, this small header ad can be edited at Structure > Blocks > Small ad ('configure' link). It is possible to disable it here. However doing so is likely to spoil the layout of the header, so if it is to be removed it may be best to replace it with another image if identical size (even if that is just a white square!) or consult the web developer.
On the new site the Cicero book ad and the Corinth book ad are displayed randomly in the right hand sidebar, as they were on the old site. On mobile this sidebar is stacked beneath the main content.
To add a randomized ad, when logged in as admin, go to Content > Add Content > Randomized Sidebar Ad, give it a title (which will not be shown but makes it findable for admins later), upload an image of the suitable size (160px wide, 600 px high), and Save.
To find an existing ad, go to Content, and use the filter to show where Type = Randomized Sidebar Ad. When you have found the ad in question, you can delete it, or you can edit it and from Publishing Options (bottom left of edit form) you can unpublish it, so as to suspend it temporarily (at which point it could be reactivated in future, or used as a template and adapted for a new advertiser, setting it again to published when it should go live again).