Frank:  Thanks for your question.  Based on the photograph you sent, it appears that the eggs on your tomato leaf are stink bugs.  I can't be sure of the exact species.  The brown marmorated stink bugs are the ones I am most familiar with; however I find conflicting descriptions of their eggs. In addition, the eggs change color as they mature.  I think what you have are most likely green stink bugs as their eggs are most often described as barrel-shaped. In any event, they can all cause considerable damage to crops so it is advisable to destroy the eggs as soon as possible.  Dropping the whole leaf with the eggs into some soapy water is the most direct method.  It would be prudent for you to monitor your tomatoes (and other crops) often to destroy any eggs that you see and to be alert for the nymphs and adults as well.  Please see https://www.uvm.edu/sites/default/files/Extension-Master-Gardener/GreenStinkBugsinYourGarden_000.pdf for additional information and get back to me with any questions.

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Frank:  Neem oil can be effective, but really only on the nymphs.  Adults seem to be resistant to even more potent insecticides.  In addition, there is always the danger of killing beneficial insects.  Knocking the adults into soapy water is the easiest approach.  Also, if you have a lot of them in one place, you might consider vacuuming them with a shop vac.  That is also something to consider if they get into the  house.  Here is a link to information on additional approaches to management and control:  https://extension.umd.edu/resource/stink-bugs-vegetables/.  Please get back to me with any questions.