Juno didn't approach the grave; rather, she remained seated until people began to mill about and fall into place to do whatever it was they were doing at the graveside. After a few minutes, she quietly started walking away from the gathering. With all the activity being confined to the immediate graveside, no one would notice that the Manticoress had departed.
She wasn't Summer, so she perceived it as not being her place to touch the casket or whatever else was going on that she couldn't quite follow. Those testimonial actions were for others to perform by dint of their Court or any real connections they had with the deceased.