Most people her use a program called MajinSS and not a greasemonkey script. However, times in general are important as that is one of the methods used to determine whether the score you send will be reviewed, and if reviewed whether the score would be considered legitimate by TNT.
The term Mod in score sending means modifier. There are games that a score needs to be divisible by a particular number. An example would be Korbat's Lab. It has a Mod of 10. This means that all legitimate scores need to be divisible by 10. There is no way to get a score that is not divisible by 10 legitimately. So when making a list that uses score ranges: i.e 100 - 180, Mod:10 tells the program or script to only submit 100, 110, 120 130, etc. Whereas Mod: 5 would make it submit a score of 105, 110, 115, 120, 125, etc. Modifiers depend on the game itself. You can find the correct modifiers in various places on clraik or on a google search in general.
I hope that answers your questions, if not, please reply with further clarification.