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If a blur filter uses a convolution, then it's invertible through a deconvolution.

There will be some information loss from edge effects and quantization noise. But mostly invertible.

You're not wrong but invertible filters, noise or no, are simply not anonymizing and should not be used for that purpose.

It can't, but blurring might remove less data than what you want.

Deconvolution is any attempt to recover data that has been passed through some known transformation. It can "create new data" because it is effectively mathematically-educated guesswork.

In the case of upscaling an image, deconvolution involves looking for images which, when scaled down, resemble the original image being upscaled. That kind of pre-image approach can be applied to blur as well (if the blur process is deterministic).

I think you may be confusing deconvolution as the term is used in neural network literature with deconvolution as defined in mathematics/signal processing.