I'm more inclined to think, that the symbol alongside the Summon Materia is categorised as an equipment, like the other two (weapons & armor) are already implying. It's not necessary to mark the Summons extra, when they're already recognisable through the red Materia colour that's only assigned for them. I reckon it has more to do with it's functioning as an additional/external slot for the weapon (it's placement is on the same row after all).
I know I will open an old can of worms (again) with this topic, but I still believe the Summons in the game's lore aren't your mass-produced type of Materia. The only man-made/artificial Summons were 'abominations' based on the original Bahamut (that's my headcanon anyway), but the process behind creating this type of Materia requires large quantities of concentrated Mako energy, and despite having a couple of successes, it wasn't efficient enough to pursue it further. To actually reproduce them naturally, one first had to acquire/find the Summons in the game, and normally there was only one of each kind available. I think the Summons, Cloud & Co. were discovering, are the same creatures the Cetra worshipped as guardians at their time. I think it was mentioned in one of the Ultimanias, where at one point they crystallised themselves for some reason. But this makes sense in a way, because in that form they will not die, therefore can't be extracted as 'knowledge' from the Lifestream, or be used for the artificial process of Materia.
Now, back to the unknown symbol. Suppose the Remake revives the concept of Summons to be guardians at ancient times, the Cetra could have built relics as a symbol of still honoring them after they used their crystallised form as weapons. These relics are meant to be a home/temple for the mystical beasts to live in, so they embedded the red orb in the relic to be used as "ancient slot" attached on your weapon of choice. That would mean, we are not finding Summons in their rough (Materia) form, but as another type of accessory.
