In all seriousness, that's actually a pretty good recruiting poster...
TBS is 6 months of infantry school. ALL Marine Officers are required to go through it after being commissioned. This is different from OCS, or "Bulldog", which all Marine Officers must go through before commissioning. I guess it could be described as "boot camp", but it's much more than that. If you're ROTC, I believe it's a 10-wk course between your junior and senior year. While not doing it myself (I'm Navy), I know it's very challenging (thus the "running with a pack that was half my weight" comment"), but most get through it.
SERE (Survival Evasion Resist & Escape) school usually takes place right after flight school and is only 2 weeks long (longer if you do something with a higher security clearance), of which only 1 wk is in the field.
I don't know about quotas for females, but I'm sure they exist. I've seen women get put in different airframes/locations just because they wanted to spread the female aviators around. The supposed quotas exist for the Navy too, however. Maybe less females apply for the Marines so they need more...
Regardless, I wouldn't worry about it in regards to you "not deserving it". Most things you get to do in the military are because they have a specific need and you qualify for it. There are plenty that could be aviators or fly the airframe they wanted but don't get it because there wasn't a need, or they didn't qualify in areas they couldn't control (eyesight, anthro measurements, etc. - in that regard, none of us "deserved" our spots, God gave them to us). If they have a need for women, take advantage of that, and be the best NAVAL OFFICER you can be.
Hope this helps.