Ok, I'm the 30 year die hard Honda/Acura snob, just kidding on the snob part. Form what I have read, learned, learnt... Honda approved P/S fluid is a different chemical composition. Honda P/S Fluid is a mineral-oil type I believe, and may very well have a bad reaction with any other type of fluid you may add that is not compatible. I have no idea what the composition of the fluid you may, or "may" not have slightly contaminated it with. It's not your pump you have to worry about, it's your rack and pinion. A bit more costly and difficult to replace than your P/S pump.
Walmart may carry Honda approved fluid, my local does not! I used to buy it there. It also used to cost me $2.00 per bottle and have recently had to buy BECK/ARNLEY for $4.00 per bottle plus shipping, so cost has go up. I never used Honda branded fluid, pffft. I never had any problems with compatible fluids and I have logged many many miles in Honda/Acura's.
I would flush it. For the few bucks its not worth risking the rack. Like I stated, the pump does not care. I have replaced a few pumps, never once have I had to replace a rack!