Donation of eggs is a complicated process. Any surgery
or medical process can make this already tricky process more difficult. That being said, depending on the fallopian tube surgery, one may still be able to donate eggs. There are many risks and benefits to donating eggs. I encourage you to talk to your OB/GYN.
The process of egg retrieval involves a few steps. First, the donating women is given hormones to help the ovaries produce many eggs during the menstrual cycle (instead of one). This is because the process is so variable--that trying to capture more than one is necessary to get at least one. Eventually, when the eggs are ready, they are retrieved. This is done with a needle that pierces the vagina and goes into the ovaries.
Fallopian tube surgery is a general term. If the tubes are cut or tied (for contraceptive purposes) then one still could donate through the above process. If there was another surgery than it is possible that the ovaries were damaged and therefore make the process less likely.
Most people who undergo the process above usually do so with their own eggs to have their own biologic child. The need for donated eggs is relatively small.
I encourage you to talk to your OB/GYN about the risks to yourselves as well as the benefits of the process. Good Luck!