I have seen many posts on both tumblr, twitter, and some message boards of EO shippers (not sure about the rest of the SVU fans, I've never seen anything said otherwise) claiming that Elliot was really reaching for his cell phone. Here's one page from tumblr to prove my point. Time to prove them wrong:
Elliot's cell phone rings. He was sleeping and didn't want to pick it up. As it was ringing, Kathy picked up despite Elliot's protests. To sum it up: Elliot did not want to pick up the phone, nor did he want Kathy to. But Kathy didn't listen...
Did Kathy pushed Elliot's hand away so he wouldn't take his own cell phone to talk to his partner? Oh wait, apparently Elliot was not at all reaching for his cell phone. He wanted to hold his wife's hand!
Conclusion: Elliot wasn't reaching for his cell phone. At all. He wanted to hold his wife's hand. The only time he wanted his phone back was after Kathy hung up so he could put it back on his nightstand. Elliot had no intentions on picking up his phone call from Olivia before, during, or after. If Elliot wanted his cell phone, then he would've done a much better effort to get it.
Sorry EO shippers but those are the facts.