Mark on the back cover caused by removal of a stapled pin. Will this be a problem when I travel?

Minor damage to a passport is likely to only be an issue if it somehow impacts any of the security features of the passport, or if it could in any way be seen as an attempt to modify the passport (including any of the visa pages) in any way.

Generally speaking the back page of the passport does not contain any such security features, nor does it contain any information that could be modified. Thus it is extremely unlikely that the damage you've shown would cause any issues when using the passport - presuming that the damage is restricted to the back cover.

Modern passports - including Egyptian passports (since 1991 according to Wikipedia) do contain an RFID "chip" that can be read wireless, and which could be disabled by such damage. However I'm not aware of any passports that contain this "chip" on the back cover of the passport - it is normally either on the front cover, or a separate page in the middle of the passport. You should be able to confirm where it is by looking for the "e-passport" logo on a page within the passport.

If the chip page is damaged then the passport is still able to be used, however such damage could lead the immigration staff to suspect that the damage was done to deliberately disable the chip, which might be a sign that the passport is not legitimate so at a minimum could be cause for some additional scrutiny at the border.