Mom had a root canal gums swollen a bump with pulse in it remain on gum why ?

Abscess or cyst: If the swelling is in the area that equates to the top of the root then it is probably a cyst or an abscess. The root canal may help to resolve this over time. If not then she will need an apicoectomy if she still wants to save the tooth.

Remaining infection?: If the problems persist beyond a few weeks, you should go back to see the dentist who did the root canal treatment.

Chronic infection: This sounds like a chronic root canal or periodontal infection. Using warm salt water rinses the bump should eventually drain like a pimple and it will feel better. The problem however is that the cause of the infection still remains. Request that your general dentist refer you to a root canal specialist to confirm the diagnosis and proper treatment.

Infection: Sounds like an infection is present and she should address this with the dentist who did the root canal.