Pwr Steering Fluid in Trans

4T60E Tranny. Hi y'all. I have an oil cooler for my trans and my power steering. in doing major repairs I replaced all the lines. I accidentally crossed 2 lines so the power steering and tranny fluid were circulating together. I didn't know and added 2 1/2 quarts of pwr st. fluid. I've flushed the tranny twice since correcting the lines. will the pwr st. fluid harm the tranny? How many times should I flush it? Using Dexron VI synthetic. Tranny fluid looks ok now, just a little thin. I am going to flush it 1 or 2 more times unless I get different advice here. Thanks for any input.
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Thanks again!
Thanks