If seeking written permission to post grades by partial UH Number, student's who decline to have their grades posted must be provided with a reasonable means for receiving his/her grade.
I don't know whether this is the worst sentence of 2007 (Miss Teen South Carolina may have something to say about that), but it is pretty bad. That first, dependent clause looks like it's missing its entire subject. Who is seeking permission? We don't know, and the main clause doesn't tell us. I'm not even sure these clauses are related—where does the permission come from, the student or an unnamed source? I'm going to assume that the author meant instructors must seek permission from students.
Moving along, “UH Number” is vague, since UH utilizes many different kinds of numbers. Of course it's possible that the author could be referring to one very specific type, since “Number” has been capitalized to make it a proper noun, but I doubt it. We can probably assume that the author meant UH Student ID numbers. Moving along, “student's” is possessive for no good reason, and pronouns shift from being plural to singular because...I have no idea. Oh and also, where are the grades being posted to? I'm just going to leave this to context, but I think if this sentence was meant to stand on its own, this would be a valid question. So, let's see if we can fix this up!
Here's my attempt at fixing it: “Instructors seeking to post grades by partial student identification number must obtain written permission from their students and provide a reasonable means of distributing grades to those who decline.”