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On a closer look, I saw that the broken stud is on the transmission side door, not on the cover. Major removal and disassembly... I think I'll leave it alone, for now.
Thing is, it's got to be sorted sometime so why not do it now before it throws other problems up? Be careful with the extractors - use only as a very last resort, break one of those in there and you'll have major problems. Personally I never use the hateful things. Based on the assumption that if the bolt won't come out by other means and you end up having to re-drill and tap the hole, it's always easier to drill the broken bolt out rather than a snapped extractor. Just my opinion of course - others may differ!
Take it to the shop and have them address it for you. If you don't, a leak will develop and the possibility of water contamination is increased.
I've done five transmission leak repairs this week and I can tell ya it is much cheaper to get this fixed now than it will be if you wait till later.
Depending on what exhaust you have, some allow access to the side door without removal, you are looking at one (1) no exhaust removal, to two (2) including exhaust removal hours of labor, max.