They can release him prior to June 1 with a post-June 1 release designation (they can do this with 2 players), but - as others have said - they don't get the Cap savings until June 2. That's OK, though, since they are going to need Cap space for Sept when the Rule of 51 Cap accounting ends (and everyone counts) and to have Cap space to carry into the season for injury replacements.
Releasing Pitta prior to June 1 saves $3.3M and leaves $4.4M in dead money on the Cap. Post-June 1, saves $5.5M this year, with $2.2M in dead money on both the 2017 and 2018 Caps. So, either way, the net savings is $3.3M and the dead money is $4.4M, so it's just a matter of how they want to account for it.
A post-June 1 release designation cannot be done unto after the start of the league year, so it cannot be done now, they have to wait until March 9.
Personally, I'm not convinced they will go post-June 1 with Pitta - if he's going to be cut, of course. The Cap savings if done before June 1 is $3.3M. That's substantial enough, IMO to cut him prior and, most importantly, not pushing dead money into 2018. In the past, the Ravens have shied away from using post-June 1 releases and have preferred to take all of the dead money in the present year.
They did do Eugene Monroe post-June 1 last year, but that was because there was $6.6M in dead money to deal with and because they had to wait until he could pass a physical before releasing him. So, that was an exception.
That said, they also have Wright and Zuttah as potential cuts and both could also be post-June 1 release candidates, so they may go with 1 (or 2) of they 3 as post-June 1 releases. It really all depends on just how much Cap space they want to make this year.