This year there are 3 situations that may happen when the team touches an active (i.e. autonomous) robot to rescue it and bring it back to Base for restart. This information comes from Rule 31, Touch Penalty, and Rule 26, Touching the Autonomous Robot, as well as the description of the Missions.
2) Basket on the robot
This is actually a complex questions this year, and I cannot give you a yes or no answer. Whether a basket is subject to the Junk Penalty depends on whether it is considered to be part of the robot or not. If not, then it is a Strategic Object (Rule 12) and would be subject to a Junk Penalty at the end of the match. Baskets that are part of the robot will not incur a Junk Penalty.
The definition of the robot in Rule 10 is very flexible. It allows any team-supplied object to be considered part of the robot if it is designed not to separate from the rest of the robot by hand. It can be joined by "any method, any configuration", which is very, very flexible. Robot attachments are NOT examined via the Gravity Test (Rule 15), which only applies to mission models. Rule 11, which defines Attachments, doesn't add additional information--it just says that attachments are sometimes part of the robot and sometimes not.
It is the referee's determination whether something is part of the robot or not. However, if your team has a strategy that you think should allow a basket to be part of the robot, I encourage your team to be prepare to discuss the rule with the table referee. And maybe alert the head referee about it prior to the tournament. (You can contact your tournament's head referee via the Tournament Director.)
A basket that "sits" on an arm and luckily doesn't fall off of the arm during normal operation of the robot would NOT be considered part of the robot, in my opinion.
A basket that sits on an arm and is restrained from sliding off the arm during normal operation would probably be considered part of the robot, in my opinion.
An basket that the robot pushes but could easily back away from would NEVER be considered part of the robot, in my opinion.
VA/DC FLL Referee Advisor