I figured out a way to solve the problem by enclosing most of the loop in the if statement checking for false of the background page, otherwise it doesn't do anything. Thanks for your help, wapperdude.
The solution is below:
Private Sub butSubmit_Click()
Dim vsoPage As Visio.Page, vsoShape As Visio.Shape
For Each vsoPage In ThisDocument.Pages
For Each vsoShape In vsoPage.Shapes
If vsoPage.Background = False Then
vsoShape.Text = Replace(vsoShape.Text, Get1, New1)
vsoShape.Text = Replace(vsoShape.Text, Get2, New2)
vsoShape.Text = Replace(vsoShape.Text, Get3, New3)
vsoShape.Text = Replace(vsoShape.Text, Get4, New4)
vsoShape.Text = Replace(vsoShape.Text, Get5, New5)
vsoShape.Text = Replace(vsoShape.Text, Get6, New6)
vsoShape.Text = Replace(vsoShape.Text, Get7, New7)
vsoShape.Text = Replace(vsoShape.Text, Get8, New8)
vsoShape.Text = Replace(vsoShape.Text, Get9, New9)
vsoShape.Text = Replace(vsoShape.Text, Get10, New10)
End If
Next
Next
Get1 = "Enter Text"
New1 = "Enter Text"
Get2 = "Enter Text"
New2 = "Enter Text"
Get3 = "Enter Text"
New3 = "Enter Text"
Get4 = "Enter Text"
New4 = "Enter Text"
Get5 = "Enter Text"
New5 = "Enter Text"
Get6 = "Enter Text"
New6 = "Enter Text"
Get7 = "Enter Text"
New7 = "Enter Text"
Get8 = "Enter Text"
New8 = "Enter Text"
Get9 = "Enter Text"
New9 = "Enter Text"
Get10 = "Enter Text"
New10 = "Enter Text"
UserForm1.Hide
End Sub