The portrait of Walburga Black was a massive inconvenience for the Order members when 12 Grimmauld Place was their base of operations, yet the most they ever did was cover it with curtains. Were there no superior options available to them?
There are so many options that would have provided a more permanent solution. The curtains could have been sewn shut, they could have painted over the portrait, they could have rubbed methylated spirits on the canvas, they could have torn down that wall and replaced it with magic.
We know that Sirius had no real affection for his mother and would have happily gotten rid of the portrait (as he had done to so many other remnants of his family's past), so what reason was there to just leave this highly distressing painting behind some easily opened curtains?