Trigger shard_of_the_true_cross_mission_anc_trigger
WhenToTest LeaderMissionSuccess
Condition Attribute Piety > 3
and PaybackID pope_rome_min_penalty_major_reward
and not I_WorldwideAncillaryExists shard_of_the_true_cross
and not HasAncType Relic

AcquireAncillary shard_of_the_true_cross chance 5

Well according to that trigger taken from the export desr ancillaries, the pope does give items when you give rome back but as you can see, the chance is only a meager 5%. Better to get your generals on crusades. The chances are 30%. If not on crusade, then its just 10%

Heres a list of rare items and the settlements you can get them from.
Spoiler Alert, click show to read: 


Catholic Items
Shard of True Cross : Tripoli
Holy Lance : Antioch
Holy Grail : Aleppo
Iron Crown of Lombardy: Milan
Bridle of Constantine : Constantinople
Holy Chalice : Jerusalem
Veil of Veronica : Jerusalem
Icon not made by hands : Edessa
Holy Prepuce : Bordeaux, Hamburg
Crown of Thorns : Jerusalem, Paris
Holy Shroud : Constantinople
Ark of Covenant : Cairo
Seal of Solomon : Jerusalem

Muslim Items

Ark of the Covenant : Cairo
Hair from Muhammeds Beard : Acre
Mohammeds Footprint : Damsacus
Holy Mantle : Antioch
Key to Holy Kaaba : Edessa
Lock of Kaaba : Adana
Sword of Muhammed : Baghdad
Holy Quran : Mosul
Soil from Muhammeds Grave : Gaza
Standard of Muhammed : Nicaea