Hi,

would this work:

 ListLinePlot[ToExpression[Transplant], Frame -> True, 
 FrameStyle -> Directive[GrayLevel[ 0.75]], 
 FrameLabel -> {"(row index)", "(in millivolts)"}, 
 FrameTicksStyle -> Directive[FontSize -> 17, FontFamily -> "TimesNewRoman", GrayLevel[0.35]], ImageSize -> Large, 
 LabelStyle -> Directive[FontSize -> 17, Gray, FontFamily -> "TimesNewRoman"], 
 AspectRatio -> 0.45, GridLines -> Automatic, 
 GridLinesStyle -> Directive[LightGray], 
 PlotStyle -> Directive[Thickness[0.0032]],
 PlotRange -> {All, {-1500, 1500}}, 
 PlotLegends -> SwatchLegend[{"Transplant"}, LegendMarkerSize -> 13, 
 LabelStyle -> 
 Directive[FontSize -> 17, FontFamily -> "TimesNewRoman", Gray]]]

I used your import functions. Note that I used the function ToExpression, because the way you import the data makes Mathematica believe that the entries are strings. This is why you see the quotation marks in the output of your array.

Cheers, Marco