Upvote:4
Every time you use your passport it's going to be up to the official in question to decide if it is damaged enough for them not to accept.
If an official says that your passport looks damaged that means they think it's at least close to the point where they might reject it. If they actually accept it that might mean they think it's not really that bad, or that they are going to accept it for now just because they don't want to cause you trouble.
You can probably keep using the passport for a long time, especially if you are otherwise a low-risk traveller who doesn't use visas or get extra scrutiny. I used a water-damaged passport for years, getting occasional warnings about how I should probably replace it.
On the other hand, it only takes one very strict official to decide the passport is badly enough damaged that they are not going to accept it to cause you some real trouble, possibly costing you the price of a plane ticket or an entire vacation, or at absolute worst a denied entry that you have to report for a long time.
Decide what your tolerance for risk is, and replace or don't replace the passport.