In the scenario you described, where a rope is tied between Earth and Mars and someone pulls it on Earth, the information about the pull would not travel instantaneously to Mars. The reason for this lies in the fundamental limitations imposed by the speed of light.
When the person on Earth pulls the rope, the information about the pull can only travel as fast as the speed of light. This means that the information needs time to propagate from Earth to Mars. The distance between Earth and Mars varies depending on their positions in their respective orbits around the Sun, but on average, it is about 225 million kilometers.
Even though the speed of light is extremely fast, it still takes time for light or any other form of information to travel such long distances. Light from the Sun, for example, takes about 8 minutes and 20 seconds to reach Earth. In the case of the rope, the information about the pull would propagate through the rope at a speed close to the speed of light, meaning that it would take several minutes to reach Mars.
Therefore, the person on Mars would not feel the pull instantaneously but after a delay, determined by the time it takes for the information to travel from Earth to Mars at the speed of light.