Identification: Egg shaped growth with zinnias. What is it?

I planted zinnia seeds in seed starter mix on 4/16. This morning I noticed several small egg shaped growths in one of the pots. They are about 4 mm tall with a depression about 1 mm acrosss on the top. They are white with a brown lip around the opening. Can anyone identify this or point me in the right direction?. I have never seen anything like it.
Thank you for your help.
(I am attaching two pictures. I kept the files small- about 250 k. If you need higher resolution please email me. )

 

Fungal spore-producing bodies. Another species might produce mushrooms.

 

They look so interesting. Are they damaging to the plants? I am worried they might spread to the other pots. Right now they are in only one. Should I remove them gently with tweezers? We have these plants in the kitchen. Thank you for your help!