I believe you should get a copy of the works orders and an invoice for the works.
The invoice would probably show an ammount due from yourself as NIL or show as being covered by warranty...
You would require some form of receipt from them in case of further issues, if the dealer was to close etc etc you would need some form of proof that the works were carried out.
Should also make sure that they have fitted what they have said will be fitted ie a new gearbox and not a secondhand or recon one...
Depending on the part in question, you may find that a new replacement part is covered by its own longer warranty than the one you have used for its replacement...... a question worth asking
Could always phone Mitsubishi directly to ask the question