I'm going to take the unpopular side and say to think about this from the perspective of the manager/center for a second. I supervise the front desk at a center, and have a different viewpoint.
Anyone can come in off the street and say, "Hey, I was bowling here a few days ago and this happened. I want it fixed for free." If this is Sunday and you bowled on Thursday, how do they know you didn't go over to a different center of Friday or Saturday and get it damaged there? One that maybe doesn't have a pro shop, or simply points at their "not responsible for damage to personal bowling balls".
Does it suck for the honest people? Definitely. But there are just too many people out there who can and do pull this sort of thing.
A small chunk missing is not going to damage the lanes. I guarantee you that they have many house balls with worse damage, and get thrown down the lanes many more times than your ball. Also, you should let the desk know immediately, so the mechanic can look for the cause, and remedy it before any other balls get damaged.
If you didn't think it to be a big enough deal to report on Thursday, then I don't see why it is on Sunday.