I can't believe people are saying a grandparent shouldn't have a snuggle with a grandchild without asking permission.
That's fucking crazy and controlling. Like, actually batshit.
Having kids means new scenarios pop up all the time. Maybe you have a routine, but a kid is sick, or wakes up in the night in a new place, or gets cold, or a train is missed and it's lunchtime, or or or.
So as a parent (or grandparent) you adapt to the circumstances and get back on track. That might mean warming up on the couch (because God forbid you take the GC into bed if the parents don't like co-sleeping) before you put him back to bed.
That is well within normal decision making parameters, it's not deliberately fucking up the parents routine. And no, it's not going to blast the child's whole routine to shit. Possibly he might be a little more tired the next day, but that is because he woke up, not because his grandmother took action to warm him up before going back to bed.
People do need to learn to live with the fact that in any given situation, a caregiver might take a slightly different approach to a solution. This happens between parents all the time, and it's fine - it's good for kids to have these normal variations in their experience with differernt people. Differernt solutions are not usually worse or better, or not that much.
And in any case - you cannot ever expect that others will even know what you would do in every situation so they can do precisely the same thing. Even if they try, sometimes they won't guess right. It's an unreasonable expectation to have of others.
It would be hellish to have to interact with a GC on that basis constantly, constantly thinking if what you say or do in a mundane situation (like a wakeful child) is what the mum would do.
Other adults who are close to a child are such a blessing to children. Unless they are unsafe people, parents gain so much for their kids by allowing them to become close to grandparents. That's in part because they are different people, children gain by having people who love and care for them, but are not exactly like their parents. Grandparents are often the first people in their lives who play this role.