[This is not really an answer, but it's too long for a comment. I'd welcome comment on this approach, which I know works in other contexts.]
I think there's an interesting approach here which, well, I'll describe it.
If you assume that whatever is is in front of the lens does two things:
- it turns most of the photons reaching the lens into random noise by scattering within the label;
- but it allows some small proportion of photons through unmolested.
Then you are clearly not going to be able to recover anything from a single image, because the noise dwarfs the signal. But if you take a long sequence of images from the camera, then you can essentially sum these images, and you'll find that the noise gets slowly washed away while the signal doesn't.
Note that this will only work for some object where at least some of the light is able to get through unaffected, which is not the case for a lens, for instance! So this isn't a deblurring approach it's a de-noising approach.
So you may be able to recover a useful image by essentially looking at a movie made from the webcam and processing that. However this will only work, even in principle, if there is a stable image to be had: if you, for instance, move a lot, then it's not going to be able to recover an image.
Still, I'd use a cover which is actually opaque.
Here is an example of this approach (in a simulation). Here is a set of 6 images: the first is the original photograph. The second one has had random noise added to it, with the noise level being a factor 100 greater than the image. The remaining images have this process iterated 1000, 10,000, 100,000 and 1000,000 times (with different random noise each time). You can see the image slowly climb up out of the noise.