Scars and similar wounds
When using the Combat section's Optional Rules: Scars and Wounds—half of which is just scars—or after having gained scars from another source,1 unless the scar's source says the scar is healed by magic, the scar isn't healed by magic. Scars aren't mentioned as removed by the spell heal, the spell regenerate, any version of the spell restoration, nor any spell like cure light wounds.2 Note, however, that scars gained via the Optional Rules: Scars and Wounds explicitly are removed by the spell regenerate.
Grafts and similar items
The Fungal Grafts from the Craft skill's Expanded Alchemy Options says that
A fungal graft can be removed with a heal or greater restoration spell, or with a successful Heal check against the original DC in another hour-long surgery.
Emphasis mine. In Pathfinder can typically means has the capacity to or is able to but need not (hence largely synonymous with may; cf. must). Thus the section on Fungal Grafts implies that a caster that targets a creature that possesses one or more fungal grafts picks whether to remove the target's fungal grafts, much like a creature using the skill Heal could elect not to perform surgery.
A creature possessing other organic replacements and additions—such as the demon senses, the demon talon, the glabrezu claw, the sin runes, and those created by the feat Inscribe Magic Tattoo—seems to keep those even if the creature's the target of the spell heal or greater restoration.3
Don't get sentimental: This is only the body you're in right now
By the time an adventurer is level 7, his friends should be able to rustle up a reincarnate spell for a dead companion, and that spell—the lowest-level spell that brings back a dead creature—brings back the dead creature "in a new body[, as t]he magic of the spell creates an entirely new young adult body for the soul to inhabit from the natural elements at hand." The spell raise dead requires a dead creature, yet the spells reincarnate and resurrection require only a portion and true resurrection but a name.
So only for levels 9–12, when adventurers have (possibly) outgrown reincarnate and have no access to resurrection, should adventurers consider their own dead bodies mildly important. Otherwise, bringing an adventurer back from the dead can get him a new identical body or a random young adult body.
By implication, then, the game expects horrible things to happen to adventurers' bodies... then the game expects adventurers to be brought back from the dead in fresh, new bodies. An adventurer doesn't own his body; he rents it until a trap or monster decides to evict him. Then either somebody finds him a new place to hang his soul for a while until he's kicked out again or he goes to his eternal reward because nobody cares about him one way or the other. So it goes.4
Self-mutilation and all that
If a character is unwillingly or inadvertently healed of permanent injuries he'd rather have kept, the GM shouldn't discourage the character from inflicting those injuries again on himself. That's weird, but, in a fantasy game that all but requires some classes to change form somehow after a certain point and expects a soul to be in a new body every so often, not crazy.5
1 Other sources of scars include (but aren't limited to) bearing a scar of desiny, casting the spell skinsend (which says that scars from the spell "fade normally with the use of healing magic"),i an encounter with the haunt ghostly brands, picking the magus arcana spell-scars, picking the shaman spirit battle and taking hp damage, removing the crown of the iron king, and the witch's hex scar (a unique case).
2 I, too, thought the various cure spells specifically healed damage without scarring, but nothing I've found says that. Just in case I was remembering a different edition, I searched the Player's Handbooks and Dungeon Master's Guides for Dungeons and Dragons 3.5, Advanced Dungeons and Dragons, 2nd Edition, and Advanced Dungeons and Dragons. Appropriately, only the Dungeon Master's Guide for Advanced Dungeons and Dragons mentions scarring:
If any creature reaches a state of -6 or greater negative hit points before being revived, this could indicate scarring or the loss of some member if you [the Dungeon Master] so choose. (82)
There's your Gygax fix for the day. You're welcome.
3 Inorganic replacements include (but aren't limited to) the mundane hook hand, the magic items clockwork arm and clockwork prostheses, and the implement provided by the trait Peg Leg. These, too, appear to remain after the creature is the target of the spell heal or greater restoration; the spell regenerate, however, may make it necessary to detach a regenerated part and reattach an inorganic part (certainly a harrowing process!).
4 Some witches have especially interesting options.
5 In View from the Edge for R. Talsorian Games's role-playing game Cyberpunk (1988), after detailing how to improve the Attractiveness attribute, there's this:
Want to decrease your Attractiveness? A straight razor costs fifty-nine cents. (43)
And there's your cyberpunk fix for the day. You're welcome. Again.
i I plan to work the phrase normally with the use of magic into a nongaming conversation at least once today.