Just a quick thought experiment before the main part of this post. A man walks on an island and leaves a footprint. Does the island therefore 'remember' the man? We would probably say not. But what if the footprint influences how a river drains, thereby changing the shape of the island? Does it now remember? What would it take to say the island 'remembered' the man?
OK. This paper (12 page PDF) is a very dense read, and if you're like me, you won't follow most of it (at least, not without a lot of background reading). But the key point stands out in the discussion: "postnatal brains continue forming synapses and neural circuits and undergo activity-dependent refinements. Egr1 has been shown to control newborn neuron selection and maturation during the critical period of a few weeks after birth." As we read in the helpful summary, "Egr1 is a transcription factor, which is a protein that helps transcribe DNA into RNA. Egr1 plays a vital role in long-term memory formation." As one commenter on LinkedIn says, "This effectively redefines memory to include antigens."
Or does it? Is every trace a memory? If we get a scar from an injury, is that a memory? If we catch a disease that wipes out our immune system, have we lost our memory? What does it mean to say a person 'remembered' an experience?