It's not a matter of gravity escaping the clutches of a black hole. Let me try and give a very oversimplified answer.
Suppose you and I and two other friends take an ordinary blanket and stretch it out tightly between us, one of us at each corner. We would have a nice, relatively flat and undistorted surface. (Pretend we did a really, really good job!)
Now, another friend comes in after a night of bowling and sets his (or her) bowling ball in the middle of the blanket that we have stretched out between us. The ball makes quite a depression, doesn't it?
This is a greatly oversimplified, but useful example of how large masses bend space-time.
Let's replace the bowling ball with an eight ball. Now there's a good sized depression in the center of the blanket, but no so much at the sides anymore. In fact, I can put a tennis ball out near the edges of the blanket and it won't roll into the center like it would with the bowling ball. But if I put that tennis ball close enough to the eight ball and the depression it has made it will roll right into the eight ball.
Of course, if a bunch of us stretched out the infield tarp at Dodger Stadium we could put the bowling ball in the middle and still have places around the edge where we could set a tennis ball and it would not be drawn into the depression made by the bowling ball.
Just like with gravity, the farther away we get from the center of mass the more weakly the object interacts with whatever else we put on the blanket.
You might think of the bowling ball as a neutron star in our example, and the eight ball as a large planet or star. The more massive the object is, the more it bends space-time and the further out it's clutches reach.
Using this example we can talk about the influence gravity has on bodies without having to resolve the dilemma of gravitational force traveling at infinite speed.
Of course, particle physics implies the existance of a gravity carrying particle, but we've not been able to get out hands around one yet. We're not doing much better with magnetic monopoles either. If a gravity carrying particle, or graviton is discovered, we will once again have to reconcile the issue of gravitational force travelling with infinite velocity.
I really hope this has helped. Please remember that I'm just reviewing the theories presented by respected individuals to explain what we observe. I'm not itching for a debate.
Interestingly enough, we are not able to prove that the natural physical "laws" we derive from what we observe are true. We can only test them and apply them. If an experiment yields results that contradict what we think we know, then it's back to the drawing board.
I mentioned that nothing can travel faster than light in a vacuum. This is mathematically true, but observation bears it out as well; in other words, we don't observe things travelling in excess of light speed in the universe around us.
In case anyone is familiar with Cerenkov radiation, the neon blue glow seen above reactor cores operating at high power, it is caused by high energy beta particles exceeding the speed of light in the water surrounding the core. It is kind of like an optical sonic boom.
This does not violate the universal speed limit of 186,000 miles per second, which is the speed of light in a vacuum.
Sorry about the long post. It's hard to explain briefly.