Try spraying with a regular mild soap solution to soften, rinsing, and then quickly spraying with a 10% bleach solution. Bleach really won't burn most plants. Leave it on there a couple of minutes and then hose it down well. You could try doing just a small branch and see how it works for you. I know this worked on smaller plants for me, as well as on my vinyl siding when the maple tree got scale.

wouldn't insecticidal soap do the same think as regular soap as far as softening the mold?

I'd be cautious about using insecticidal soap......it can cause phytotoxic reactions with many plants. Would be a shame with all your efforts to control the aphids and their honeydew, just to lose the foliage to phytotoxicity :-) Test on a small branch first. And I'd never recommend using bleach. Period.

Otherwise, horticultural oils can help to loosen sooty mold as well as control the aphids - neem oil or all season paraffinic oil could help. Hose down the tree well after application (given a reasonable time for the oil to work) to remove whatever mold has been loosened.

And sulfur can help to prevent the growth of sooty mold. Recommended application rate is 2-4 lbs of wettable sulfur per 100 gallons. Warning: Do not use the oil and the sulfur simultaneously or apply the oil while the sulfur is on the foliage -- that WILL create a phytotoxic reaction.

Good luck.

I'm sorry but I suspect you will not find any of that effective in removing sooty mold already present. I was growing a small crop of ornamentals inside a g'house and due to the thick foliage canopy and my own laziness for not scouting sufficiently, aphids got ahold and by the time I had a handle on them, the sooty mold had already progressed. I had to gently hand wash each and every leaf on the plants with a soap solution to remove it, and even then it didn't come off easily. You can use it to prevent the growth of sooty mold, but once it's on a leaf, it has a glue-like property and won't be 'sprayed' off.

gardengal, woudn't spraying after sunset and rinsing the next morning reduce the chance of phytotoxicity?

I thought I had read that sulfur and soap is safer than sulfur and oil.

Calliope, "You can use it to prevent the growth of sooty mold, but once it's on a leaf," What can I use?

I guess I was trying to say...once the mold is on the plant, you don't get it off. You can arrest the growth of it, but short of individually hand-washing each leaf on your linden tree with soapy water and cotton balls, I am saying the black reside is on for the life of the leaf.