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Hello @lilyen
Unfortunately it is not possible to add a link to a background image, as the web standards do not provide this ability.
What you may want to do is implement the header logo element – https://creativethemes.com/blocksy/docs/header-elements/logo/ – and link to the homepage that way. That should do it for you.
Alternatively, if you know your way a bit around HTML, you may use the HTML element – https://creativethemes.com/blocksy/docs/header-elements/html/ – to insert an image and link it to anywhere you may want to, including the homepage. The TinyMCE editor from that should be able to do this.
Hope this helps!
Thanks.