Exhaust problems are usually obvious from the noise made.
Loud roaring usually means a hole in one of the pipes. Rattling can mean part of the system is loose (or that something else under the car is adrift and making contact with the pipes). Tinkling or can-rattling type noise can mean a problem in the silencer.
If your exhaust isn’t making any of these noises, you should ask the garage if work really is needed. If you’re satisfied there’s a problem, remember you will probably only need to replace part of the system, and not the whole exhaust.
Sometimes it can just be a mounting, so if in doubt get it checked before further damage occurs. Regrettably, the lack of road maintenance in recent years has led to widespread damage to wheels, tyres, suspension and exhaust systems.
One final note of caution is that many tyre and exhaust centres have low wages boosted by part sales. So it pays to find an honest and dependable repair shop, where you won’t be persuaded to pay for unnecessary work.