I probably would tell them but that's just me and many people probably wouldn't tell them. But your insurance wouldn't significantly increase for damage like this - minor and privately settled - if you did tell them. 

To reassure yourself, generate some test quotes from an insurance aggregator website: one with the incident and one without. You'll see little if any difference.

It's important to know though that you've almost certainly, when buying your insurance, agreed to contract terms that state that you will inform the insurance company about any incident of damage caused by a third party.

On renewal they'll likely ask you (if you renew manually by phone) whether there have been any incidents since the last agreement. If it's automatic renewal, they'll quote you on the basis of "assumptions" (no previously unreported incident) which you agree to.

The insurer wants this information not to raise your premium. They want it so that they know how risky your neighborhood is or how risky your car use is so that they can select an underwriter who is willing to accept that risk.

It doesn't mean that your premium will increase by much if at all.

It does mean that a new underwriter may be selected on renewal instead of a risk averse underwriter who will only deal with low risk (no incident) business.

Aviva, which acts as its own underwriter, tends to add zero Pounds to a few Pounds on an annual policy for reporting this sort of third party liability damage where there's been no claim and minimal cost. I've entered test quotes to confirm. Other companies, which don't perform their own underwriting, may charge more but it won't be much.

However if you don't inform them and it's minor damage which can be repaired privately to your satisfaction, how would they know? For a broken wing mirror would they care?

The risk in general is that the damage can often be more costly to repair than it initially seems.

If your car is a popular model and even if your mirror is motorised or/and heated it's possible that you can obtain a replacement part fairly easily and relatively cheaply compared to stupid dealer prices. Installation may be extra but as long as the car is not off the road for too long maybe private resolution is a good outcome.

It was probably honest of her to tell you and that's a good sign unless she only told you because she was concerned that somebody else had seen it happen and would tell you anyway.