Depends on the kind of blur. Some kinds can indeed be almost perfectly removed if you know the used blurring function, others are destructive.
But, yes, don't take that chance. Always delete/paint over sensitive information.
Source: we had to do just that in a course I took a long time ago.
Ah man, I remember when they caught some pedo creep who used a non-destructive blur on the CSAM materials he produced that included his face. So satisfying.
wouldn't you also need to know in what kind of pattern the blur was applied. I am sure if you do it multiple times starting from multiple non identical partitioning of the region, it will be impossible.
Actually not always, there is a script that can recover text from mosaic'd screenshots if the font and pixellation technique is known. I just use a fake mosaic – the easiest way is to paste a bitmap of non-confidential text from elsewhere in the screenshot and then apply the filter.