We consider in this work a variant of the Steiner Problem in Graphs (SPG) with the additional restriction that terminal nodes must have degree 1. We customize the Greedy Randomized Adaptive Search Procedure (GRASP) metaheuristic, testing its performance on a large problem set obtained by modifying 182 SPG instances from the SteinLib repository. The GRASP obtained good results, with low average gaps with respect to known lower bounds in most of the problem classes, and attaining the optimum in 44 cases (24% of the problem set).