After all my upper left teeth were extracted a month ago today i noticed there is a pea size or bigger hard lump on the outer side on the back tooth?

Bone defect: Surgical removal of multiple teeth in the maxillary region can create an alveolar bone defect. Tooth extraction is a traumatic procedure initiating a complex cascade of biochemical and histologic events that inevitably lead to a reduction of alveolar bone, soft tissue and bone defects (exostosis). These defects will be addressed before future teeth emplacement.

Post extraction: Healing , specially multiple teeth creat a boney crater with raised edges, a month is not enough for complete healing and tissues might fill in and turn into bone latter, if implants are intended for example, you might need a bone grafting and ridge augmentation before the ridge be able to receive any implants.

Bump post ext: If the lump is hard and feels like i tis moving under the tissue it may be a boney sequestrum--sort of like a bone splinter. It may also be a subperiosteal infection. When in doubt--go back the dentist who extracted your teeth for a follow-up ASAP. .

Post extraction: You will feel bumps as the bone heals and the socket fills in.if this bump,is soft or movable or if you have pain then see the dentist and have the area checked. Are you wearing a denture now? This may need adjustment. Call you dentist if you are concerned.

Bump = ?: What you are seeing and feeling may be a number of things from normal (such as bone exostosis) to minor issues to some things that are require treatment sooner rather than later. I advise you see the dentist who did the extraction (and the restorative dentist, if both are involved) to personally examine you, determine what's going on and advise you accordingly. This is part of routine aftercare.