They made this one a real PITA. Here's what I did in 2014:
1) Open SolidWorks
2) Tools --> Options --> System Options --> Colors
3) Look at what's listed next to "Default scene:" - mine said "00 3 point faded"
4) Close SolidWorks
5) Open a Computer window and browse to C:\Program Files\SolidWorks Corp\SolidWorks\data\graphics
6) Make sure the Scenes folder and subfolders/files are not read-only (right click Scenes folder --> Properties)
7) Go into "Scenes" folder then "01 basic scenes"
8) Right click on "00 3 point faded.p2s" and edit with Notepad
9) Make the line that starts with "floor" read as follows:
floor visible nonreflective "Materials\miscellaneous\studio materials\shadow floor.p2m"
10) Add the following line just before the line that says "end"
floor_reflectivity 0.000000
11) Save the file and close it.
12) Open SolidWorks again
13) File --> Open. Select "Template" instead of "All Files" in the file type dropdown (just above Open and Cancel buttons). This should take you to where the default part, assembly, and drawing templates reside. Select Part.prtdot and click Open.
14) On the right side of the screen, click the tab for "Appearances, Scenes, and Decals" (looks like a 4-color ball).
15) In the upper pane, make sure Scenes is expanded and click the Basic Scenes folder underneath it.
16) In the lower pane, move the slider till you see "3 Point Faded". Click, drag, and drop onto the model background. The "Appearance, Scenes, and Decals" flyout will disappear.
17) File --> Save
18) Repeat steps 13 through 17 with Assembly.asmdot
This should keep the floor reflection from showing up in new parts and assemblies. If you have any old parts or assemblies that still have floor reflections, you can just use steps 14 through 16 on them.