It is possible the "S" stands for the Company, Sierra. The "4" may be fourth Platoon of Sierra Company, or fourth Battalion that the company is part of. "BRT" could stand for Brigade Recon Team, which would be the infantry element of a reinforced Marine regiment, or Marine expeditionary brigade. The 1/7 could either be 1st Battalion, 7th Marine Regiment, or 1st Regiment, 7th Division.
Better information can be gleaned indirectly from Halo: Evolutions. As E2 from E2-BAG/1/7 means Eridanus II, S4 may actually be a planetary designation. If this is true, then the unit could have been originally stationed at Sigma Octanus IV, or at Mars (Sol, IV).