I see the weekly timelog review from last week, but I need to add 15 more hours to last week.
When I click add manual time and then travel back to last week, the add manual time button hides. How can I do this?
I believe it's not possible to add manual time for a work week that has already passed. Your best bet is to talk about it with the client and just do it for another day.
Michael is absolutely correct, you missed the cut off time, which is 12 noon UTC (!) on Monday.
After that the work diary locks and the client is billed and charged, that is why changes can no longer be made afterwards. It makes sense, but clearly it's a pain for you right now!
Talk to your client, explain what happened. Depending on the weekly limit for the job the client may need to increase yours so you can add 15 hours that should have been in last week's, plus whatever hours you may be working and adding this weeks.
In general clients seem to prefer it if Freelancers don't add their hours at the very last minute, so they can plan what they will be charged the following Monday, so it might be useful to add hours as and when you work them rather than all at once 2 minutes before the deadline.
This would (obviously) also avoid the current situation of you not being paid for last week until a week after you would have done....