No actual experience with a Jazz, but it seems quite a reasonable price considering the amount of work involved. (potentially) Replacing the clutch at the same time (even if it still had a few more miles left in it) is also sensible.
However the main concern is exactly what is meant by the claim the gearbox is 'reconditioned'(or similar words such as 'rebuilt' etc) as this can have a considerable affect on the cost .
. There are four basic options.
1) Brand new. Extremely expensive. Impossible for £1300.
2) Fully reconditioned . Here the gearbox is stripped down by an expert , and a large range of bearings, oil seals, gears etc are replaced with new part as a matter of routine, whether they need it or not. This is also quite expensive. Unlikely to be possible for £1300 IMO.
3) Repaired. Your gearbox is stripped down and only those parts found to be worn or damaged are replaced. Maybe just one bearing. More likely to be possible for £1300 inclusive of the other work.
4) Replaced with a used gearbox from another car that it is hoped will be in good condition. This is the cheapest option but risky as the replacment may also be faulty.They are unlikely to give a very long guarantee.
The price difference between all four options is large. And its always possible that an unscrupulous garage will deceive a customer, claiming its reconditioned, when in fact its only repaired, or a used unit. Even the fitting garage may themselves have been deceived by a 'gearbox specialist' who sold it to them as 'fully reconditioned ' who in fact only repaired it.. Rebuilding gearboxes is quite specialised work. Some general garages might send your gearbox away to a specialist for repair/reconditioning. . .
Its also possible that even with a genuine and honest garage there has been some breakdown in communication with the customer as to the exact definition of what work has been done on the gearbox.