What to do about a hen's clumped back end?

The short answer is yes....sorry to ruin your day. You can use the kitchen sink or a plastic tote or the bathtub. Try to get it extra warm in the room you use and the water temp ideally should be about a hundred degrees. You dont have to get her entire body wet if you dont want, you can just take the sprayer or shower head and shoot her bottom. If she is a furry bottom breed like a cochin, you can trim some of that down from her rear and help her in the future

I had a similar problem- poop got caught up on my Silkies bottom. I used a warm disposable wash cloth- dampen with water and mineral oil- it helped to soften the poop ( which got rock hard!) and  it came right off.  Good luck!

Ugh....I have the same problem with at least 1 of my girls....maybe 2.  I have to get in there and wrastle them out to get a really good look.  Tired of having poo eggs.  I'll be bathing chickens I guess....also not my idea of a good time.  Oh wait....it may be!  Unless of course she gets loose in the kitchen and goes flopping her poo butt all over the place. 

I believe the term you're looking for is "pasty butt" and, yes, you can give her a bath to loosen it up.  It usually happens in baby chicks and can be a cause of death if not taken care of.  For an adult hen, you may want to consider trimming her vent feathers after the bath to help prevent it later down the road.  Another trick to try is adding a tablespoon of apple cider vinegar (ACV) to their water.  But it most definitely needs to be cleared away or it can cause her to get egg bound!

How does the ACV help with pasty butt?  I need that explained to me.

You can cut the clump off too just be careful. The butt feather will grow back in.

Same thing happened with one of our girls last year.  We affectionately called ours "poopy butt".  When it got bad we'd turn her upside down and trim it off with scissors.  This is a 2 person job, though.

We also fed her yogurt mixed with her pellets.  She loved it and helped regulate her tummy/poop.

The idea is that the beneficial bacteria in the vinegar (it has to be the type with live cultures) will improve conditions in the digestive tract and that will improve the texture of the poop... but this is presuming that the problem is that the poops aren't normal.  It's more likely that your hen simply has a very fluffy rump or an abnormal tail (my mom has a barred rock with wry tail that gets manure clumps...)  Cutting the feathers short near the vent will help.  And if you cut rather than plucking, you won't have to repeat the job until she molts.