If it's only clamps, you do have a chance that a doctor could remove them laparoscopically without a lot of fuss. You're in better shape than someone who also had the tubes cut and cauterized. But you'll still need to stay hyper-alert to the issue of ectopic pregnancy (an embryo that gets stuck in the Fallopian tube). Know the symptoms and get checked early, if you do have the clamps removed and then get pregnant.
As Trying said, no amount of "going really deep" will dislodge the clamps. They're off to the sides, not in the vaginal region.
I don't think there is any way you can reach those clamps. They would have to be removed but a Dr I would imagine