I just finished using a grease gun on my tiller. As usual, it everything is greasy and putting it away without getting everything greasy can be a challenge. Here is my solution and it doesn't cost anything.
Step 1: What Do You Need and What to Do.
Depending on how how you work in the garage, you might have used this with your current greasing project. If not, you probably have a box of them. What you need is a nitrile glove.
What I did was to put the tip of the grease gun into the finger of the glove and stretch the glove over the end of the gun.
And now you have the grease gun ready to store without getting everything greasy.