For the most part, the eggs are fairly secured to the mother's tail. However, if you stress a mother too much and she tail flicks to escape or get loose, that can shake a lot of the eggs free from her tail. Irrespective of being in or out of the water.
If you need to move her to view her or to put her into another tank, I suggest picking up one of the those small breeder tanks that sit on the inside of a normal tank, a large tupperware, etc and gently making her back into and then view/move her. You know, rather than actually handling her in or out of the water.