Pita gia Souvlaki is not an order at the counter so much as a specification for the bread itself: the pita sized and built for wrapping, as opposed to a flatbread you tear and dip. Across Greece this is the round used for souvlaki and gyros to go, and the whole sandwich depends on it. When a shop's wrapped order falls apart in your hand, the bread is almost always the reason, and it is the variable this entry is about.
The right pita for wrapping is a soft, pliable round with no pocket, somewhere around a hand-span across and a few millimetres thick, sturdy enough to hold a packed filling without splitting. Good practice is to brush it lightly with oil and pass it over the hot griddle or the edge of the gyros grill for a few seconds a side, so it picks up a little char and color and turns supple rather than crisp. A well-warmed round goes soft at the fold and takes a tight roll; the cone holds, the base seals, and nothing leaks until you have eaten down to it. Sloppy execution shows up as a pita served cold and stiff straight from the bag, which cracks along the fold the moment it is filled, or one left too long on the heat until it dries to a brittle shell that shatters under tzatziki and juice. A round that is too thin tears under the weight of meat and patates; one that is too thick and bready turns the whole thing stodgy and buries the filling.
Because it is defined by the bread and not the contents, this round is the platform every wrapped variant sits on. The same pita carries gyros and grilled souvlaki skewers alike, and it is the reason a to-go order can be eaten one-handed at all. Some shops keep a thicker, fluffier round for plated merida service and a thinner, more flexible one specifically for wrapping; others use a single round for everything and simply griddle it longer when it is going on the road. Thessaloniki-style shops often favor a slightly thicker, oilier pita than the leaner Athenian round, which changes how tightly the cone packs. The skewer-based sandwich it most often wraps, souvlaki proper, deserves its own article rather than being crowded in here; what matters at this entry is the bread, because get the round wrong and there is no sandwich to wrap at all.