This is a known iOS - Safari issue that works somewhat by design: dragging operations propagate to the Body part of the page HTML in iOS devices. As a result, the solution that applies to every other device - to simply hide the background with a grayout overlay - doesn't seem to work there.

Our team hasn't yet identified a workaround that is both comprehensive at addressing this and would not risk breaking other elements in unexpected ways when more complex scenarios are applied.

In the meantime, this can be mitigated by making a popup be taller than the whole screen height. This will mean that the popup becomes scrollable on top of the page, instead of just showing a scrollable background page. You may also simply hide the background page by using an opaque overlay if you want to hide that inconsistency.