A creature that possesses the type undead cannot normally be targeted by the spell atonement because of the atonement spell's entry of Target: Living creature touched (also see Aiming a Spell on Target or Targets). The supernatural ability rejuvenation of an edimmu presents an exception to the way the spell atonement normally works but only for a creature that possesses the rejuvenation ability. As also explained in fine answers here and here, the game routinely makes specific exceptions to the general rules as part of its design.
This means that a cleric, druid, or inquisitor can't cast an atonement spell on your undead PCs unless that caster possesses a special ability that allows the caster to overcome the limitations of the atonement spell's Target entry.
That should answer the question. However, if you're interested in how difficult it is to send incorporeal undead genies to their final reward using the far-too-brief exception made by the rejuvenation ability then read on.
A strict reading makes it extremely difficult to use atonement to send an edimmu to its native plane
The supernatural ability rejuvenation of the edimmu—an incorporeal and undead genie—, in part, says, "The only way to destroy an edimmu is with an atonement spell. The atonement absolves the creature of its sins and sorrows, allowing it to finally return to its native plane." Hence the edimmu's rejuvenation ability does create an exception for the atonement spell, but it's a far smaller exception than it may perhaps initially appear.
That is, even with the exception made by the edimmu's rejuvenation ability, a strict reading still doesn't change the atonement spell's entry of Target: Living creature touched as the rejuvenation ability makes no exception for the atonement spell's Target entry. Unless the less-strict reader extrapolates, speculates, or make house rules (a term I don't use pejoratively), exceptions change only what they say they change, and the only change to the atonement spell when an edimmu's (somehow) the subject is that the edimmu may opt to return to its native plane.
Thus it's the atonement spell's caster who is left with the uneasy task of somehow targeting with that atonement spell a creature both that possesses the type undead and that's probably destroyed. (And after these targeting obstacles there's the extraordinary ability incorporeal and its 50% miss chance against corporeal effects.)
Nonetheless, the vast amount of material available for Pathfinder means that I have no doubt that a specific set of character options allows a caster to cast such an atonement spell. However, I suspect that set of character options won't be present in most campaigns (except, of course, in regions and settings overrun by edimmus).
Finally—and not inconsequentially—, the edimmu's original and (so far as I'm aware) only treeware appearance is in House of the Beast (2009), part 2 of the Legacy of Fire adventure path that Paizo published for Dungeons & Dragons 3.5, and House is for level 5 PCs that by the adventure's end achieve level 7. In other words, it doesn't matter that in the adventure where edimmus actually appear as antagonists that an edimmu can be returned to its native plane only with an atonement spell: the PCs that encounter them won't typically have access to atonement spells anyway. (The atonement spell is usually available only to characters level 9 and higher.)
What this all adds up to for this reader is the humble suggestion that perhaps the rejuvenation ability of the edimmu is actually an error… of sorts. I mean, the ability as it's presented does—if tilt your head and squint—function mechanically, but for an adventurer to reach the goal of that specific atonement spell requires leaping through how many flaming hoops exactly? Honestly, typical adventurers could very well find it easier to destroy forever a lich than to redeem and send home a bothersome edimmu! (And the typical edimmu is only CR 3!)
I suspect somebody involved with House of the Beast—likely somebody late at night on deadline—forgot (or forgot to care) that the spell atonement had that Target: Living creature touched entry. This wouldn't be the first time that Paizo seemed to fail to realize how abilities and exceptions to them work (for example, see this question and this question) or that special care must be taken when designing effects for undead creatures (for example, see this question).
In the end, a GM that wants to use edimmus in a traditional campaign may want to make a house rule like A creature can cast an atonement spell on the remains of a destroyed edimmu as if those remains were a corporeal living creature, but the reader should be aware that this is a house rule. Another GM may see things differently, expecting characters who took specific options to thwart her campaign's edimmu invasion.
Note: As an example, the spell-like ability second chance that's the level 8 granted power of the inquisition Redemption specifically does circumstantially overcome any targeting restrictions on the atonement spell that the spell-like ability largely emulates when the second chance ability says that "you can cast atonement as a spell-like ability, targeting a creature that has violated the tenets of a religion you both share or that freely desires to convert to your alignment." (An incorporeal miss chance continues to apply to the typical corporeal caster, though.) Still, because of the level at which it becomes available, even this special ability can't help PCs who are fighting their way through House of the Beast, but the second chance ability may be useful against your campaign's undead PCs.