Was Hajar (peace be upon her) buried in "Hijr Ismail"?

Naming the Hijr as "Hijr Isma'il" has no basis. Ibrahim and Isma'il built the Kaaba completely, including this area of the Hijr. When Quraysh rebuilt the Kaaba, they fell short of pure funds, so they excluded the Hijr from it and built a low wall around it. This is as reported from Aisha, may Allah be pleased with her, that she asked the Prophet, peace and blessings be upon him, about the wall (al-Hijr), "Is it part of the House (Kaaba)?" He said, "Yes." I said, "Then why did they not include it in the House?" He said, "Indeed, your people fell short of funds."

It has not been proven in any Marfu' Hadith (definition) that Isma'il or Hajar were buried in the Hijr. The reported weak narrations (athar mawqufah) that suggest this are improbable.