This is the original image:
Screenshot of the contaminated result of the blurring
Screenshot of the available result if countermeasures are applied:
Cut and paste the area that you like to be blurred into 2 new layers. Use Paste special > Paste in place to avoid shift. You should save the selection because it vanishes too soon. Save also a spare of the cutted and pasted area into a third, hidden layer. You, at least in the beginning, will miss it.
You must load the selection back before blurring. If you do not, the blur spreads. Probably you want the blur to spread somewhere. There you should expand the selection before blurring. Draw the expasion area by polygonal lasso or other selection tool and press Shift simultaneously.
Blur the upper of the new layers Erase another new layer partially by eraser; you probably like to save something near the selection border, because there is anyway some transparency contamination (as you say) from outside. Quite surely you must reduce the opacity of the lower new layer or use the eraser with smooth brush and reduced opacity (say 25%) to retain continuous look near the border.
If you want only to get rid of contamination and don't care discontinuity, then leave the partially deleted layer off. The contamination will be replaced by the background.