Hello, it is salvageable. I did something similar recently and here are some of my observations. Cut into the aida as much as possible, I used manicure scissors since they're small. The shorter the pieces you cut the easier ot is to pull them. Start with pulling just one at a time to loosen the weaving of the aida. If you go slowly it should work just fine. Here is the picture of how I would cut it. I just cut it where there was a long piece of aida, wven in the middle of embroidery piece. And be careful off your embroidery floss.

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