Here's the corrected sentence with the proper grammar:
"Do you know that these gloves have been lying around all week?"
Here's why:
* "Lay" vs. "Lie": "Lay" requires a direct object (something being laid down), while "lie" doesn't. Since the gloves are not laying anything down, we need to use "lie."
* "Lying around": This phrase means to be in a place without a specific purpose.
* "Have been": This shows the gloves have been in this state for an extended time (all week).
Let me know if you have any other sentences you'd like help with!