Cleaning up gray mess around text?

[Ofnuts]

Obtaining this:

   

The process:

• Use Filters > Enhance > Wavelet decompose (max lelvels: 7)
  
• Make all decomposition layers invisible, then make then visible one by one from the bottom 
  
• You eventually get some kind of smear that covers your text (level 3 here)
     
  
• Open the channels list, and drag any of the RGB channels in the list below to copy it(*)
  
• Make it visible and apply a threshold to isolate the text
     
  
• Right click and Channel to selection
  
• Add new layer at top, and fill selection with white
  

A slightly simpler way is to apply a Gaussian blur instead of finding the appropriate level of wavelet decomposition, but I find it a bit less accurate.

If necessary you can use Curves in the result to add a  bit more contrast without being bothered by the murky background:

   

(*) Warning: this deselects the channel that you dragged, so click on it to re-select it otherwise later changes won't apply to it (for instance painting with white will appear purple if you dragged the Green channel).