As you may or may not know, backflushing on a LM or Synesso is about blowing clean (or detergented) water through the drain-side of the 3-way solenoid valve, as well as the distance between the shower-head and the 3-way valve.
On the Linea/FB70's and older GB5/FB80's, it's a relatively long distance: from the shower head, down the banjo tube, out the side of the group neck, and around to the 3-way solenoid (which hangs like a pendant-necklace below the group neck). It's a long distance to have to blow water out of... maybe an ounce of volume?
On the newer GB/5's, FB/80's (with Piero caps) and the Synessos, that distance is a lot shorter. This is one of the reasons that the gicleur/flow-restrictors on the Piero-capped LM's need to be smaller than 0.6mm to produce a similar pressure ramp-up. The location of the solenoid is also why there's more water dripping when you kick-off the group on a Piero-capped LM with the portafilter out.
The difference between backflushing with the screen in or out... well... people know I'm all about bizarre, irreverent analogies... so here it goes: backflushing with just water (or detergent) is like going pee-pee. Whether or not you have the screen in is pretty much irrelevant. If you were to go #2... well... ok, forget it. I'm abandoning this analogy right here.
The point is, if you were to try to brew espresso with the screen out, when you kicked off the group, a quantity of the water-soaked grounds would get blown/sucked up into the tubing. Normally, there's a screen in place to keep (most of) the grounds out when you kick off the group. The 3-way solenoid is fairly small in diameter where the action happens in the valve itself, and it'd be pretty easy to muck it up with even a small amount of coffee grounds... but it'd have to be a lot more than you'd normally encounter when backflushing after removing the screen.
That all said, I think that if there's a rule of thumb here, it's that you should always do your best to keep the shower-head and group gasket area clean. This includes having strong group screens. Weak screens will pop up and let grounds sneak in around the dispersion screw hole, which could mess up your machine, and dirty your shower-head area. I also see a lot of baristas flushing their groups, but not nearly enough that wipe the screens too.
Ed, best-case, in my personal opinion, backflush with the screens in
. Not because you'd hurt the machine otherwise, but because it forces clean water up and down the screen, possibly dislodging some particles from the mesh in the screen (can you say, "lessons learned the Clover?"
). Merely soaking the screens in espresso machine cleaner won't dislodge particles as well as backflushing with the screens in would. However, backflushing with the screens removed won't hurt. Just keep the areas clean!