How can one convince people who say that there is no strict prohibition mentioned in any hadeeth for reciting Surah Fatiha or Qur’an at the graveyard?

They interpret the evidence from the hadeeth of Aishah (رضى الله عنها) that shows the analogy of those houses where Qur'an is not read as graveyards, to say that the hadeeth refers to the dead people and has no clear prohibition mentioned in it.

The person who says reciting Surah Fatiha is allowed in the graveyards is the one who must provide proof for that and not the one who is forbidding it.

When it comes to ‘ibaadah (acts of worship): the principle is that everything is forbidden until there is proof to show otherwise. Reciting the Qur'an or part of it is an act of ‘ibaadah and thus we will need proof to show us when it should be recited.

To say that the hadeeth is referring to the dead people and in no way refers to the prohibition of reciting the Qur'an in the graveyards is a false analogy/qiyaas.

The similitude given by the Prophet ﷺ is not for what happens in the graves but it is for what happens in the houses and homes.

In brief, until there is authentic proof to support the recitation of the Qur'an in the graveyards, the ruling should be the original ruling: It is forbidden.[1]

Only Allah knows best.

Reference:

[1] http://islamqa.info/en/11938