It's like they're doing it to bother you, it's nothing to do with the kids - as though they can justify their actions by telling themselves "well, we always sent birthday presents"
^This.
I have a SIL like this. We've had no contact with her for a decade following an appalling betrayal of trust between her and DP (her brother). She has never acknowledged what she did, so no apology or amends. On a couple of occasions the PILs have engineered a meeting between DP and her by ambushing him/us with her attendance at some event or get-together and DP just turns around and leaves. That's the scale of the problem, to give some background. She has no relationship with the kids even though they were all born before the incident in question. She has seen DS1 a few times (mainly in connection with her wedding, at which he was an attractive pageboy-shaped accessory) and DS2 once or twice. She has never seen DS3 even though he was about 18 months by the time the falling out occurred. That's how interested in them she was - not that I required her to be interested in them, or us.
But since the falling out she's religiously sent them birthday and Christmas presents. They are always impersonal, partly because she doesn't know anything about them and partly, I suspect, because she gets her secretary or nanny or someone else to sort them out. A huge gift token is a typical example. I hate it. As a pp said, it's an intrusive reminder of unpleasantness on an otherwise happy day, and is quite clearly designed to stake a bizarrely misguided claim on the moral high ground. As for how to explain to the kids, well, I just told them the unvarnished truth when DS1 asked once. Just told the story, exactly how it happened, no interpretation, no editorial. If she imagined they were one day going to get in touch and want a close relationship with her, she obviously hadn't pictured that scenario.
It's tiresome and attention-seeking and I wish she would just give it up.