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Carl Woll
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Just use Show instead of Overlay:

Show[
    bg,
    ListPlot[
        MapThread[
            Callout[#1,#2,"CalloutStyle"->Directive[Thick,Red]]&,
            plain
        ],
        PlotRange->{{-180,180},{-90,90}},
        Axes->None,
        PlotRangePadding->Scaled[0]
    ]
]

enter image description here

Carl Woll
  • 131.7k
  • 6
  • 246
  • 359