Looks like our GE
let me guess, and water is dripping into the refrigerator? Sometimes it is necessary to replace that drain trough from underneath / behind the evaporator coil. But, there is a more likely problem. If you pull your refrigerator out from the wall, you will see a black 1/2" tube coming up from behind the machine compartment cover. at the top of this tube is a black, drain diverter, which has an outline in the mold similar to the elbow underneath your kitchen/batroom sink. 90% of the time this diverter gets clogged with gunk, preventing the water from going down that 1/2' tube to the pan under fridge, instead, it drips down the back wall of your refrigerator, pools under the crisper drawers.
To see if this is your likely problem, while holding the diverter firmly against the back wall of the refrigerator, you dont want to damage the plastic "hooks" that hold it firmly against the back wall...holding that diverter, grab the middle of the 1/2" tube, or to prevent some splashing of yucky water, grab it closer to the diverter and bend the tube towards its middle, while pulling the tube out of the bottom of the diverter, you wont have much, if any water coming out, maybe an ounce or two. leave the tube as it is. Now slowly rotate the diverter clockwise, less than a quarter turn, you will feel it loosen when the "hooks" have cleared the tabs in the opening. take this diverter to the kitchen sink, and pour some water into the large hole, does the water come out the bottom, where it would normally feed into the 1/2" tube? No? thought so. keep rinsing and shaking the diverter, you will see all kinds of gunk come out, shake it REALLY good, tap it against the sink, loosen up everything. go back to the fridge, look up into that hole, pull out any gunk you see in there, put the diverter in the same position it was when it released, turn it back counter clockwise, while holding it in place, put the 1/2" tube into it, and voila.
however, if you didnt notice any gunk in diverter, and water went through before cleaning it out, then it is possible, that the rust in the drian trough has a SMALL hole, which is bypassing the plastic tube that feeds water into the diverter, thereby dripping into the fridge, THEN you will have to have your trough replaced, BUT, because of the process required to remove and replace that trough, you could cause serious damage, and lots of money to fix, and any company shouldnt charge you more than around $150 to do that.Thats what I would charge you.