I have my grandmother's costume pearls, and a couple of years ago one of the glass beads in the middle of the strand broke somehow. I went to a regular jewelry store & paid about $70 to have them restrung. They were double strand & graduaded which made it more expensive, I'm sure. The clerk warned me it would cost more than they were worth to fix them, but sentimentally they were worth way more. Single strand, same size, in US (vs Canada) would probably be less than half of what I paid.
Anyway, the point is that it's totally possible to have costume jewelry repaired at a regular jewelry store that does repairs.
However, exchanging them for a new strand is by far the easiest & cheapest thing to do!!