You'll have to magnify the area where the text is overlapping the image so you can work in close.
Then use the eraser tool (Hint: you can make the eraser smaller or larger by using the "[" for smaller and "]" for larger -- those are square brackets, by the way) to erase the old text but leave the area where the graphic is alone. You will probably have to retouch the graphic to make it look like there was nothing on top of it.
Once you save a graphic as a JPEG, it's flattened and all of the items, text and graphics, are in one "plane" or layer. Therefore, you have to edit around the graphic, removing everything that's not wanted and then retouch, if necessary, everything that is wanted.
This is quite close work and you'll need to take your time to carefully remove the old stuff.
This is another reason to save the original PSD files. Their layers will also be saved enabling you to edit stuff like this without the exasperating need to erase and retouch to to edit text.
Dennis
Dennis Hays Information Design