As seen on screenshot, buttons from quark management located incorrectly and interfere with crafting in the backpack. Is it possible to fix this?

It's not possible

While I realise this is a closed issue, if you include some files from the Quark API, it should be possible to implement the interface "IQuarkButtonIgnored" in the relevant GuiScreen that will allow you to have Quark not place any buttons at all. This would presumably prevent the issue the reporter is having with crafting interference. This appears to be an example of someone including the api although not specifically using this interface.

In previous versions I believe they had some API calls that allowed for more precise positioning of the buttons but that doesn't appear to be the case as of 1.16.4/1.16.5.