How do I get the slimy clumps out of my bisque?
One possible option might be to pick out as many of the vegetable chunks as you feel reasonable, then puree the rest.  You'll end up with a thicker soup body, and fewer vegetable chunks, but it might not be a bad tradeoff to get rid of the lumps.

Or (depending on amount and proportion of liquid to vegetable) strain the liquid out, manually add the vegetable chunks from your strainer to the soup, and either discard lumps left in the strainer or puree them with leftover vegetable chunks (depending on how much patience you have for sorting) with reserved liquid.

Last option - if the lumps are pretty visible, you can pick them out when you see them - for example, when serving from a pot into a dish, or each time you pull it out of the fridge.  If the soup is liquidy you could try scooping up spoonfuls of broth with as many lumps as you can, and ladling them into a strainer held right over the pot, so the liquid will flow right back in and only the lumps get held back.

These last are really annoying, and a lot of work, but if it's really bothering you it does help... I did something similar with a dish once, though it was for woody herb bits, since I didn't want to waste a pot-full of food.