My wife was at a wedding recently,and at one point realized that the buckle from her belt got attached to a woman’s dress. She doesn’t know whether the woman backed into her, or whether she tried to pass and got attached. She realized that the buckle caused a tear in the dress. She wants to know if she has to look up the woman and offer to pay.
Where there is a doubt as to whether a person caused damage or not, and there is no way of proving it, there is no obligation to pay.
In this case, there is a doubt over whether your wife caused damage for which she is liable, or whether the other lady backed into her, and she would not be liable for the damage. Therefore, she is not liable for the damage.
However, if the lady in question (with the torn dress) would know for certain that the damage was inflicted on her, and there is no reason to suspect her, it would be correct, latzeis yedei shamayim, to pay the damages to the dress.
In this case, it appears that the lady with the torn dress does not know for certain that you caused the tear, and therefore there will be no obligation at all to pay.
If the lady is totally unaware of the incident, and there is a chance that after being informed, she will be able to make a definite claim to the damage (knowing that she didn’t back up), it is correct to inform her. However, this is a remote chance, and in pricniple it appears that there is no obligation to take further action.