Use a screen reader to be sure that your offscreen content is hidden
Hide offscreen content from assistive technologies
You are not supposed to expose every singular element to assistive technologies such as screen readers: you should expose only relevant ones.
Offscreen content can and should be hidden from them.
How can I test and possibly solve the problem?
Use a screen reader to be sure that your offscreen content is hidden: indeed it should not be able to report it.
If you need to hide offscreen content, simply use visibility: hidden or display: none to remove the elements.
<button class="remove-me">Can't reach me with the TAB key!</button>