Hi Alfred,

Thank you for your question.  Thatch is defined as:  "tightly intermingled layer of living and dead stems, leaves, and roots which accumulates between the layer of actively growing grass and the soil underneath. Thatch is a normal component of an actively growing turfgrass, and as long as it is not too thick, it can increase the resilience of the turf to heavy traffic. Thatch develops more readily on high-maintenance lawns than on low-maintenance lawns."

It appears from the pictures that you do have thatch on your lawn.  It is very common and your lawn may benefit from dethatching.  The University of Massachusetts Extension suggests "to determine if a lawn has a thatch problem, cut out a small, triangular- shaped plug of turf several inches deep and examine it. Note the spongy layer of material above the mineral soil. If this layer is more than 1/2-inch to 3/4-inch thick when you compress it, you should consider having your lawn dethatched or beginning a management program which will encourage decomposition of the thatch layer."

One suggestion is not to dethatch your lawn when it is wet.  Since we have an abundance of rain right now it might not be the best time.  Although, spring and fall are the best time for dethatching.  

Unfortunately, I can't recommend any company for lawn care.  If you are able, you might try raking a small area at a time to remove the thatch.  There are special rakes available to dethatch or a metal rake you may already have may do the trick.  Also, some companies rent equipment to dethatch lawns.  

I hope this helps!  Happy gardening!

Home Lawn & Garden: What is Thatch? | Center for Agriculture, Food, and the Environment at UMass Amherst