We cannot rule what the driver must do without hearing his side of the story. We can give you tentative guidelines about what we think you should do, although we are limited by partial information, including regarding the specific laws and practices of your locale.
People often decide not to inform their insurance company regarding minor damages; we leave that decision to you. While someone who causes you damage cannot force you to receive money from insurance and exempt him,[1] it is nevertheless sometimes the right thing to do.
A paid worker is a shomer sachar (a paid watchman) over the employer’s property that he is working with,[2] which means that he is obligated to pay even when damage is only marginally his fault. The gemara explains that the worker is considered a paid watchman because he benefits from the object being under his guard, as it enables him to earn his wages. Therefore, even if the accident was not an outright act of negligence, the driver should ostensibly be responsible in your case.
However, other sources present an additional perspective. Until now we have discussed the halacha, but there is also the spirit of the halacha. The mishna[3] and gemara discuss the case of one who was hired to transport a barrel and broke it along the way. R. Eliezer says that the porter must swear that he was not negligent, and he is then exempt. R. Yochanan[4] explains that according to the strict law, the porter should have been obligated to pay, as a shomer sachar is exempt only from oness (circumstances beyond his control), which is not usually the case when breaking a barrel. However, the Rabbis instituted a possibility for the porter to be able to exempt himself by means of an oath, because otherwise people would not agree to transport barrels. In parallel, there is a discussion among poskim regarding a household worker who damages an object in the house during her activities.[5] The Aruch HaShulchan[6] writes that according to strict din,[7] the worker would be obligated to pay, but “the minhag of upstanding homeowners” is to not make a claim unless the negligence approached the level of purposeful damage. The extent to which one can apply these rulings to your case is up for debate, and a dayan would have to sort through all the details and indications if asked to rule based on strict din.
However, there is yet another element of the case to consider. We understand that the standard ruling in the United States (although there are likely differences between states) is that one who borrows a car with permission and then causes damages is exempt from damage payment, and the liability falls on the insurance company. This is relevant because Halacha is more likely to apply the law of the land in monetary disputes between individual Jews in cases in which the two entered in an agreement in such a manner that they implicitly accepted the local standards, which are based on local law.
Without hearing the claims of the two sides, we cannot make a determination on the matter here. However, we will say the following in a general manner.
Let us assume that you paid the youngster as you would an experienced driver who you could trust with your valuable car and that you paid him enough that it would be worth his while to take the job even considering the possibility of having to pay car damages (without your insurance kicking in). If that is the case, it is fair to demand payment for his apparent negligence. However, if you paid minimum wage (or perhaps less), having in mind that it was still worth a youngster’s time to get paid for a little menial work, it is evident that he would not have taken the job if he knew that his hard work could be wiped out by a simple mistake. If that is the case, we feel it is not menschlach to make a claim against him for the damage, and this is even clearer if you could charge your insurance if you so desired. If the negligence was of a reckless nature, of course, the story would be different.
There is an additional pertinent question in the gemara’s case – whether the porter who broke the barrel is paid for the job that he ended up not doing successfully.[8] However, in your case, the job for which the young man was hired (the deliveries) was completed, and he therefore clearly deserves his pay.