Globalization does not necessarily have to have a huge impact on the environment. However, it seems likely that it will have such an impact.
The only impact that necessarily has to happen is the impact caused by transportation. In other words, the trade caused by globalization will impact the environment. The extra air and water pollution caused by emissions from ships and airplanes and trucks will have an impact on the environment.
Much of the other impacts on the environment that seem to go with globalization are really caused by increases in demand all over the world. It is possible, however, to argue that globalization makes the world as a whole richer. If that is the case, then globalization causes the environmental impact brought on by that demand. For example, globalization causes an increase in China's wealth and, thereby, an increase in the demand for energy in China as people buy more cars and more appliances. China then burns more coal to make electricity and more gasoline to run its vehicles. This impacts the environment.