The nurse said the wound in Mom's foot was not infected. Should I believe her?

"Changed the other day " is not good enough. Get your gloves on nurse and check it NOW. Is your mother diabetic? Did she have a fever? Could you see any swelling?
You mentioned bowel issues. Were the investigated properly? The reason I ask is because patients with cancer in their digestive system develop an extremely putrid small on their breath in the days and weeks prior to death. Do you know how the foot was injured in the first place? Definitely follow up vigorously this is not trivial.

Ketones?

There is a smell I have noticed a few times on residents who are soon to die. My mother had that smell & had just got diagnosed after not even thinking she was sick except for some bowel issues after having travelled for an extended time. Thought it was restraint food, unusual for her to eat such fair, that upset her system. Within a few months she was gone.

Not to say that that is what you smelled, just that the body gasses off all the time thru the pores & even foods, inadequate WATER flushing the vital organs can cause some infrequent but noticeable odors. Infection odors have their own smell....ask others to investigate discreetly on your behalf. Not all staff have good noses.

I would demand the wound cultured. MRSA smells though if bandaged will not small as much. Following a foot surgery to remove a cyst, L developed MRSA that led to two weeks in the hospital, amputation of a toe, then three weeks of rehab.

Did the nurse mean that the dressing had been changed the other day AND that it did not smell infected the other day? And when exactly was the other day? And what did the nurse think might have been causing this noticeable odour?

I don't think you did anything wrong, I suspect instead that the nurse was an idle so-and-so who was glad to fob this off on the next shift (assuming she got round to mentioning it at handover time), but I wouldn't drop it either. When are you next visiting your mother?

I guess that depends upon several factors. What kind of smell? Have you noticed it before? What was it from on previous occasions? What kind of "wound"? Bedsore? A dressing was changed " the other day"? I'd call the night nuse who is going to check her over and get a full report.

I hope that there is a wound care doctor managing her wound.