I wonder in what circumstances (if any) the OP would consider it not suspicious to delete text messages from one's phone?
a) you keep ignoring the call log records
What do you mean by this? Incidentally, can you point me in the direction of the raw data showing the deleted call history? I have seen something which lists 4 calls to Kate, and their duration (very short, I think the longest is 20 seconds) but it is not clear from the list that these are deleted calls. This is not a trick question, I just would like to look at the "damning" evidence for myself.
b) hmm, maybe not in the first few hours of your daughter going missing, perhaps?
Why not? What would act as a trigger for you to decidde to delete your phone messages? You've made it clear that it certainly wouldn't be the expectation of receiving a large quantity of new messages, so what then?
You clearly think it is highly suspicious that Gerry deleted his call history of calls made to his wife on the night of the 3rd May. Can you suggest any reason why he would want to try and hide the fact that he called his wife from the authorities? I can't think of one (as far as I'm concerned he was probably out and about searching, calling back to Kate to see if Madeleine had been found) but then you're so much cleverer than I am so are bound to have a perfectly plausible theory for this nefarious act. 
I can only believe you're being deliberately obtuse. I mention the call records as you were flippantly commenting about it not being suspicious to delete text messages - hence "you keep ignoring the call log records". You do understand the difference, right?
All the data relating to the calls is in my initial post. Is that the 4th or 3rd time I've mentioned that in this thread now? It shows the difference between Kate's retrieved calls from her phone memory and the ones actually made/received using the network provider's data.
You still can't see that anyone supposedly in grief and panic in the first few hours after the disappearance of their daughter wouldn't normally be worrying about deleting call records and/or text messages? Amazing.
I have NO idea why Gerry was hiding details of calls to his wife and calls to what I think turned out to be the hospital. I only know it appears he did it. I also have no idea why Kate deleted many more calls/text and yest left a couple. Maybe to try and make it look less suspicious? Who knows. There's also the issue of the "missing call record" when Gerry was seen/heard on a phone and there's no record of the call on the network logs. He was using someone else's phone and as he subsequently made a call to his wife, I find that odd as his was working perfectly normally. Taking all these things together I agree with the PJ finding it significant and I'm sure they intended doing a lot more digging.
I find you and your associates' dismissal of this as utterly incredible. If any of this kind of evidence existed against Amaral for one of your witch hunts you'd be burning effigies of him by now.