Upon entering a Devil Room, a white inverted cross will appear above Isaac's head. If Isaac goes to the next floor with the icon still above his head, he will gain a Soul Heart and +1.0 damage.
Taking anything generated by the room (items or consumables) will result in the icon going away, including opening Red Chests / Black Sacks.
Notes
After Isaac has taken a Devil Deal, while a Confessional or Sacrifice Room would give an Angel Room item, it has a higher chance to spawn Redemption instead. This is the only way Redemption can be naturally generated during a run.
Using Birthright as Eden has a small chance to spawn Redemption.
If Act of Contrition was taken after taking a Devil Deal, Redemption is not guaranteed to spawn.
If there is an item in a Red Chest, the icon will not disappear, even if the item is taken.
Opening Red Chests that have been spawned after room generation, e.g. as a room clear reward or enemy drop, or opening them with Magneto, won't remove the icon.
Picking up items made free through usage of items such as Coupon or a Credit Card will still remove the icon and provide no benefit.
However, swapping out a free active item for another that was already held will not remove the icon.
Taking free pickups/items that spawned after the room was entered (e. g. room clear rewards, drops from Fire Places, rewards from Devil Beggars) will not remove the cross.
Taking pickups/items spawned by Keeper's Box inside the Devil Room will remove the cross.
Devil's Crown: Devil Treasure Rooms will count as regular Devil Rooms for the purposes of this item.
Found Soul: The soul will receive a cross when a Devil Room is entered, and will not lose it when Isaac takes an item/pickup. When Isaac goes to a new floor with the familiar having the cross, the soul will receive a damage boost (even if Isaac doesn't) and a Soul Heart, allowing it to survive multiple hits.
Jacob and Esau: The cross will only disappear if the character holding Redemption takes something. The other character is free to take items and pickups.
Satanic Bible: Taking a Boss item that was replaced with a Devil Deal will remove the cross, however the Boss Room doesn't give the cross.
Tainted Lazarus: Only the character initially entering the Devil Room will receive the cross over his head. The character that leaves the floor with the icon above his head is the one that gains Redemption's benefits.
Using Flip inside the Devil Room will make both forms have the icon over their heads. Even if one form's cross is removed, the other's is unaffected.
Ghostly items that were already bought from taking a deal can safely be taken without deactivating Redemption.
Devil Room, a white inverted cross will appear above Isaac's head. If Isaac goes to the next floor with the icon still above his head, he will gain a 
Soul Heart and +1.0 damage.
Red Chests / 
Black Sacks.
Confessional or 
Sacrifice Room would give an 
Angel Room item, it has a higher chance to spawn Redemption instead. This is the only way Redemption can be naturally generated during a run.
Death Certificate, or using 
Spindown Dice on 
Spirit Shackles.
Eden, 
Tainted Eden, or any character with 
Eden's Blessing.
Birthright as 
Act of Contrition was taken after taking a Devil Deal, Redemption is not guaranteed to spawn.
Magneto, won't remove the icon.
A Lump of Coal or 
Head of Krampus after 
Krampus fight will keep the icon.
Coupon or a 
Credit Card will still remove the icon and provide no benefit.
Fire Places, rewards from 
Devil Beggars) will not remove the cross.
Keeper's Box inside the Devil Room will remove the cross.
Black Market or 
A Pound of Flesh affected 
Shop will not remove the cross.
Devil's Crown: Devil Treasure Rooms will count as regular 
Found Soul: The soul will receive a cross when a Devil Room is entered, and will not lose it when Isaac takes an item/pickup. When Isaac goes to a new floor with the familiar having the cross, the soul will receive a damage boost (even if Isaac doesn't) and a Soul Heart, allowing it to survive multiple hits.
Jacob and Esau: The cross will only disappear if the character holding Redemption takes something. The other character is free to take items and pickups.
Satanic Bible: Taking a Boss item that was replaced with a Devil Deal will remove the cross, however the 
Boss Room doesn't give the cross.
Tainted Lazarus: Only the character initially entering the 
Flip inside the Devil Room will make both forms have the icon over their heads. Even if one form's cross is removed, the other's is unaffected.
Redemption's appearance when active.
