We discuss the nonlinear rheology of telechelic gels formed by triblock copolymers with short hydrophobic end blocks (the stickers). In this first paper, we merely study the variation of the extraction time of a sticker from a hydrophobic aggregate with the chain tension. Using a model potential that binds the sticker/chain junction point to the aggregate/water interface, we explicitly show that the extraction time only depends on the chain tension at the junction point. The results are extended to more realistic potentials by heuristic arguments. At this level of description various effects (curvature of the aggregate, sticker flexibility, impenetrable aggregate constraint) can also be accounted for.