Accidentally got trub in keg

So, I recently upgraded a few of my fermentors to the Spiedel plastic tanks. I was following the thread on those tanks on this forum, and was taking advice as to what people were doing with them.

I brewed up a Kern River Citra 2IPA about 4 weeks ago, and fermented it completely in the spiedel. For the dry hopping schedule, I moved it into my Keg and used the Dry Hopper sleeve from Stainless Brewing.

But, when I transferred the beer out of my Spiedel to my Keg, I did not siphon, I used the spigot on the bottom of the fermentor ( as someone on the other thread suggested), but that did not work out so well.. I got some of the trub into my keg... I went with it, and threw the keg on the gas after the dryhopping was done. Last night, I pulled my first pint, and there was quite a bit of sediment in my glass... so much I had to pour out the first glass. The second 1/2 pint was much cleaner, but still a good amount of stuff at the bottom. Can I expect this to clear up, or am I going to be drinking this thru the whole keg? Is there anything I can do to filter it out while I pour into a glass? I was considering lining my beer glass with a paint strainer to catch the gunk, then pull it out of the glass... Not sure if this will cause heavy foaming of the beer or not..

Or, maybe I just need to RDWHAB and have some grainy pints?

It will clear. Just don't move the keg too much or you will mix it back up. Also, expect the last runnings to have crap as it comes off the sides.