Indeed, it seems that wavelet decompose Filters > Enhance > Wavelet-decompose... does not like transparencies (I never tried on a transparent image before, though)
To push further your experiment I even exported the layer with transparencies to png without keeping the color on transparent in the export settings and... wavelet-decompose did put a black background instead, even though, my BG color was white
Thus I would recommend that instead of deleting the transparent area, make a mask save it in the channel
Then put that mask at the layer-group "folder" (or use the deleted area to make a mask via alpha to selection, then Select > Save to Channel, then add mask from channel)
BTW, those are sweet rhinos
To push further your experiment I even exported the layer with transparencies to png without keeping the color on transparent in the export settings and... wavelet-decompose did put a black background instead, even though, my BG color was white
Thus I would recommend that instead of deleting the transparent area, make a mask save it in the channel
Then put that mask at the layer-group "folder" (or use the deleted area to make a mask via alpha to selection, then Select > Save to Channel, then add mask from channel)
BTW, those are sweet rhinos
Patrice