Why is the 了 particle not used? "realized" is a completed action. The speaker does not continue to realize, he or she realizes something once, and then the action is complete. So why is it not "我发现了我没有旅游签证"
It may be one of those cases where it works with or without the 了. Or it may be that some verbs by their very nature are instantaneous and hence don't need or don't take the 了.
"我发现了我没有旅游签证" was accepted as of the date of this post.
檢 (inspecting/examining) + 証 (certificate) = 檢証 (visa)
Don't think I've heard visa called “检证". It's always 签证.
发现 can also mean "to discover".
I.e., "to find out".
"旅游签证", otherwise fine.