For several years, DH and I have endured a difficult relationship with his parents, including several months of no communication last year. However since the birth of our son (their first grandchild), who is now almost three months old, relations have significantly improved and they genuinely seem to care and be making an effort with him and us.
We've so far seen them three times since DS's birth, but video call weekly due to living a fair way from them. They've also recently acquired a new puppy which they dote on and treat like a child, and therein lies the issue. Every time we've called or seen them, they always draw comparisons between our baby and the dog, be it behaviour, sleepless nights or milestones, and often in ways to downplay our news. When we told them DS had started smiling for example, their response was to inform us their puppy had started 'smiling' 
. Every time we send them photos of their grandson, they respond with images of their puppy and saying how 'similar' they both are. MIL frequently refers to it as their second grandchild and DH's 'sibling', and how much she's looking forward to them 'growing up together'. They know that DH and I've never had any interest in dogs, so do not particularly appreciate these comparisons between our baby and an animal on a daily basis. DH has gently tried to hint this on several occasions, without wishing to offend them and cause a further rift, but so far without much success.
Would we BU to tell them of our dislike of these comparisons the next time it happens? I appreciate the dog means a lot to them, but would prefer not to have it given the same level of importance as their grandchild, every time we see them.