If you notice Google associating items/artworks/pages to your website, even when it no longer exists on your site, it is happening due to the way Google processes sites. Do note, this is not an instant process.
To map the internet and build their search engine, Google 'crawls' the internet regularly to build up its index. This is a detailed picture of what content exists on the web and how it is linked.
You can click here to read more from Google about this process.
Crawling and indexing happen periodically, and it could even be some weeks between times that Google crawls your site.
This process is entirely up to Google and not something Artlogic is able to control. This means that content deleted from your site can take some time to disappear from searches, even if it is no longer visible on the main site.