The holes are close enough that the new screws will probably go back into them, although at an angle. The downside is the heads of the screws will likely not sit flat inside the strike. I haven't seen a case where that hinders functionality (as the door can not be that tight in the jamb and still close anyway) but it isn't the most aesthetically pleasing thing in the world. If that doesn't bother you, don't worry about it.
If you wanted to resolve it, whittling down a wooden golf tee or shim until it fits in the old holes is one option. Just wood glue them in and cut off any extra length sticking from the hole. That will allow you to drill new holes without the bit finding the old ones. If you really want to get fancy you can use a vix bit to make sure it is centered in the hole.