What we are getting at is Gods that love little furry animals won't like you sending in little furry animals to trap spring, even though said animal doesn't die and yes, does go back to it's plane of existance or wherever it came from.
These Gods dislike this because:
*Poof*
*the pretty little celestial squirrel chitters at you, it's big bushy tail bobbing up and down as it looks at you with big brown eyes*
OK little cute thing, um...You want a nut? *you toss the nut onto a trap you have found, a Deadly Spike Trap in the middle of the forest path. The little creature licks it's lips and sniffs after the nut, and then pounces on it. It looks so happy and in love with the nut that you really feel for it as sharp jagged spikes of death and destruction rip into it's flesh, impaling it, causing it to squeel in pain and anguish as blood sprays into the air and portions of it's bowel strike you in the face.*
*It's mangled form though is not dead, and in the instant before death comes for it like a welcome release from it's suffering you caused it a tear rolls down it's furry cheek and it disappears back to it's home. Safe and whole perhaps, but emotionally scarred.*
*No longer will this furry forest friend ever, ever reach for another nut. The emotional scars run too deep. Never again will it trust a -insert PC race here, or any humanoid for that matter. Unfortunately, celestial nuts are all it can eat...so it dies a slow agonizing death from starvation.*
And Eldath cries for the next 1000 years because that particular one you happened to summon was His favorite. He used to hand feed it nuts daily, and now it's emaciated little form lies forever on his celestial window stoop.
Do you really want to make Eldath cry?
//and yes, I know it should have no recollection, but I used it to over-emphasize the fact that even though the animal is whole that you still -did- cause an animal creature to suffer. In fact, you tricked it into suffering, because it has a crappy Int score and really just responds. It's that aspect that rubs those Gods the wrong way.