Teams will try to take advantage of whatever little tidbits their advanced scouting can give them, and individual players can try to exploit anything they happen to pick up on other players, but you're usually not going to see the sort of extensive game-planning that you would find in a playoff series. You can only tweak so much systematically (especially at ES) when you're playing three games a week or so. There will be some special teams strategies discussed before each game, and maybe some tweaks to try to improve what the team is doing at ES, but you're usually talking about general concepts. Strategies against specific players on the other team is usually more along the lines of what sort of line match-ups you think are favorable as opposed to specific X-and-O tactics designed to exploit individual tendencies.
Personally, I haven't picked up on anything that teams are doing to specifically attack that pairing in a different way. It's just some uncharacteristic individual efforts that are standing out. Dunn gets undressed after Burakovsky pulls a sweet move one on one. I've seen Doughty get walked like that or worse more times in a handful of viewings than I can remember Dunn getting walked like that all year. Parayko being out there didn't affect that at all. Backstrom beating Parayko for a rebound goal in front of the net is another recent example of an uncharacteristic individual fail that has nothing to do with what Washington was doing systematically, or with who his defensive partner was on the ice. A few uncharacteristic turnovers, and, well, you get the idea.
The goalies playing poorly isn't helping the optics of how the defense is playing, either. The Burakowsky goal basically went right through Allen. I would never crap on Allen for the goal given Dunn's gaffe, but it truthfully ended up being a very stoppable shot. Both of them were out there for the Martinsen goal, which was terrible and wasn't their fault at all. That's already a decent chunk of the goals scored against that specific pairing the last couple of games. The goalie makes one or both of those saves, and we're probably not having this conversation right now.
Honestly, the worst play I can remember involving them the last few games was the Chaisson goal off a pass that went through four Blues right up the middle of the ice. That was just a bad goal on the skaters part, but again, it was an isolated incident. That might have been something that Washington drew up based upon how the Blues were playing, but it wouldn't have been something that was implemented solely to target and exploit the Parayko/Dunn pairing.