To remove the dew claw on a dog or not to remove it is strictly the decision of the owner. Here's a few tips.
The problem of tearing a dew claw is more likely to happen with a hunting dog or trail-walking dog than a house pup. Rough terrain is almost always the reason for the tear. On occasion a house dog can tear it if snagged on furniture or bedding.
Normally small tears around the dew claw go unnoticed and the dog gets through it just fine. Often we don't even realize the dog has slightly injured himself. Sometimes the only hint that something may be wrong is frequent licking of the area. Severe tears in the dew claw are much more noticeable. Deep tears can bleed quite a lot implying a worse injury that what it really is. Apply direct pressure to get the bleeding to stop. Often treating the torn dew claw is simply a matter of taping it down until it heals, changing the bandage often and using antibiotic ointment in the area. Don't be surprised if the dog limps quite a bit during recovery. The injury is quite painful to animals and a vet might prescribe a mild pain reliever.
If the claw is nearly torn off it can still sometimes be saved. Treating an injured dog can be treacherous at times. Dogs that normally are easy going and would never hurt a flea can suddenly snap when someone is treating them for an injury. Be careful when tending to the injured animal yourself even if you think you know him well. Wrap gauze around the claw area and use tape to hold the claw securely.
Sometimes after having the dew claw torn nearly off the owner decides to go ahead and have it removed. The dog is given a general anesthesia and the claw is cut the rest of the way off. A stitch or two might be given at that time and the paw wrapped. If your dog is schedule to have another type of surgery it's a good time to make the decision to have the claw removed but is not an absolute must.
Whether you've chosen to remove the claw or not keep it trimmed along with other claws. Regular trimming of the dew claw will lessen the chance of accidental injury. If you notice the claw is torn decide if it's severe or minor. If it's severe consider taking the animal to the vet and having it removed once and for all particularly if it's not the first time the injury has occurred.