Ask Mr. Smarty Plants

Removing the yellow leaves is really not the issue. The question is what caused the leaves of that one particular plant to yellow. Those yellow leaves are likely dyiing and will fall off on their own. Since the other desert willows you have are doing okay, we can hopefully eliminate soil problems causing the leaves to yellow. Most often, we associate yellowing leaves with chlorosis. We can only wonder if this was all a problem in how the tree was planted, rather than where.

The first thing from your question that makes us grit our teeth is that you planted all 4 trees in the summer. To us, the wonder is not that one tree is suffering, but that 3 are surviving well. We always recommend that in hot dry climates, like Texas and Arizona, trees be transplanted in the coolest months of the year, November to January being our usual choices. The very top of the list of tree-killers is transplant shock. You say the fourth tree was smaller than the others; it may have already suffered problems from being root bound after being in the nursery pot too long, or having had root damage during transplanting. Already weakened by some pre-existing problem, it really had no chance.

The second most frequent reason we cite for yellowing leaves is chlorosis:

From a previous Mr. Smarty Plants answer on chlorosis:

"Yellowish leaves could indicate chlorosis, or lack of iron being taken up by the plant from the soil. This is often caused  by poor drainage and/or dense clay soil, which causes water to stand on the roots. Again, this could  be a problem caused by planting, perhaps without any organic material added to hole, or damage to the tiny rootlets that take up water and trace elements, including iron, from the soil."

Please read this article from the University of Illinois Extension on chlorosis. Note the comment that the presence of chlorosis is often due to high alkalinity in the soil. You can be pretty sure that your soil is alkaline, but plants native to your area are accustomed to that soil, and should be happy with it.

Among the steps we would recommend are to use some sort of iron supplement, not too much, as native plants do not ordinarily care for fertilizer. Water less, because it's possible the main problem is lack of drainage in soil where the plants are growing. Watering once a week should be adequate.  Finally, using a good quality organic mulch, spread the mulch over the root area without allowing it to touch the trunk area. This will protect the roots from heat and cold and, as the mulch decomposes, will add some material to the soil to assist in drainage.

The third problem we ordinarily cite is whether or not the plant in question is native to the area where it is being grown but, as it happens, this USDA Plant Profile Map of Chilopsis linearis (Desert willow) indicates it is native to Yavapai County, AZ and therefore belongs where you are growing it.

Frankly, we don't know for sure which of our three theories is causing the yellow leaves; possibly none of the above. But we have given you some precautions about avoiding such situations in the future.