TCP data vs HTTP data over GSM modem
This evidences how each one of us sees the internet from his point of view. Starting by some basics have a look at this picture:




  Image Attribution : Chunte7 [CC BY-SA 3.0 (full license)]


As you can see the internet can be divided into 4 layers, some times 5 by dividing the network access layer into other two layers, that are in the image on the right. The general structure of any given network is the OSI model which divides any given network into 7 layers.
Now please have a look at the following image: 




  Image Attribution: Microchip devloper help


See the difference? HTTP is an application protocol that runs above the TCP protocol from the transport layer. In fact, in order to create an HTTP connection, you would have to implement an HTTP Client/Server on your system. This is sometimes taken for granted by the sysadmins since a lot of servers are easily deployed and/or implemented in Linux/Windows. When you are dealing with embedded systems this is not always the case since a module might provide an HTTP Client/Server, such as the ESP32 family, or be limited to a TCP/UDP server.

My advice would be to check for the service running on the remote server and implement whatever is compatible with what is already deployed there. If it's a completely new project and you are starting from scratch, look at your embedded system resource to see if it allows an additional layer to be implemented or not.

Keep in mind that implementing a protocol over HTTP would make it easier for back-end developers on the server and would become more scalable and features-rich. On the other hand, it will add a significant overhead for the data you are transferring and would eat a bit more resources from your embedded system.

Having a quick look at your particular module form here in section 11 you have already some TCP/IP commands so there is no need to build it from scratch, on the other hand if you go the HTTP route you would have to implement an HTTP Server/Client compliant application.