There really is no way which is why pick plays are illegal. We just have to hope the refs call them on it early enough to make teams think twice.
No, there are ways to combat pick plays but there are risks if it's not done correctly.
The 2 CBs on the side of the field with 2 WRs can switch off coverage. They can play a 2 man zone or switch off in man based on the routes. The switch off can work well; however, if they are not on the same page, it can end up with 2 CBs covering the same WR and nobody covering the other one. They did use this coverage in the past but Claiborne often failed to do it correctly and Scandrick could be seen after the play yelling at him and trying to explain what he should have done.
Another method is to play tighter press coverage to make it difficult for the WR setting the pick to get between the CB and the WR. The downside is that if the CB does get picked, then he can't get in position to make the tackle after the catch.
Just a simple mix of man and zone could help but Claiborne has always struggled with zone because it is more mentally challenging.
Something that they could do on occasion is to put a hard hit on the WR setting the pick. The problem with that is that defensive players are way more likely to get called on plays with contact than offensive players. Nevertheless, when some of those small WR like the Patriots have are setting picks, big CBs like Carr, Jones and White could ring their bell a couple of times.