I agree that a text, call or message is absolutely fine. Making a four year old write letters for six weeks after Christmas seems like overkill to me. Also, is the upset son an adult? If so, getting upset over something like that also seems rather dramatic. The letter was from a young child, for heaven's sake. she's not old enough to deliberately snub him.
It is 100% not the job of a grandmother to remind teenagers to thank other people. I do thank people for gifts, and brought my children up to do the same. When they grew up they were sometimes a bit lax - just typical teenagers with their heads full of other things - and when they left home I didn't even know when or whether they got gifts from other people. My mother used to keep on at me about whether X liked her present or if Y had worn his new shirt yet. I had no idea, as they were miles away. They would always say thank you but usually when they next spoke to her, so it was more a conflict of expectations than rudeness or ingratitude. I'd be even less likely to know if my hypothetical grandchildren got things, and absolutely wouldn't get involved in anything like that. It can take the pleasure out of the whole thing.
I don't know why people get so het up about presents. I was ill around my last birthday, and hadn't spoken to my mum for a couple of weeks, as I was sleeping a lot and generally under the weather. When I was better and spoke to my sister, she said that Mum hadn't called me as she was waiting for me to ring to thank her for my birthday present! As it was, I just had a virus, but she didn't know that - I could have been at death's door and she wasn't going to call me because I had been given a gift and hadn't thanked her. Ironically, she had handed me the gift in person a couple of weeks before my birthday (so she knew I had got it safely) and I thanked her then.
I completely understand wanting to know if a parcel has arrived, so I am careful to let people know if they have sent me something by post, but when I send to others I use registered delivery where you can track it.