The offer gives EU nationals the right to become British citizens over a specific time frame. The ECJ will not be given jurisdiction on any matters concerning them post brexit.
It would be highly unlikely that any british government would be willing to compromise on this, and so this part of the negotiation will be swift I think. But as I said, May's offer also gave the EU an indication that the UK is serious about ending 'free movement of people', and this is what seems to have bothered Merkel and Macron more than anything. These two will be the important ones to watch during negotiations, as the EU officials like Tusk, Junker, Barnier etc are just puppets.
If you listen to what Merkel is saying here, she is happy about May's proposal regarding EU citizens living here, but of course it points to an end of free movement after the five years, and this is where we'll see a strong response by the EU down the line. With a divided parliament right now, it'll be this issue about trade and immigration that's going to be making all the headlines later in the year.