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like @Greg said in his comment - you can make it really short with LINQ and you don't have to check any ranges:

static IEnumerable<T> Remove<T>(this IEnumerable<T> items, int startIndex, int count)
{
 return
 count > 0
 ? items.TakeWhile((x, i) => i < startIndex).Concat(items.Skip(startIndex + count))
 : items.TakeWhile((x, i) => i < (startIndex + count + 1)).Concat(items.Skip(startIndex + 1));
}

like @Greg said in his comment - you can make it really short with LINQ and you don't have to check any ranges:

static IEnumerable<T> Remove<T>(this IEnumerable<T> items, int startIndex, int count)
{
 return
 count > 0
 ? items.TakeWhile((x, i) => i < startIndex).Concat(items.Skip(startIndex + count))
 : items.TakeWhile((x, i) => i < (startIndex + count + 1)).Concat(items.Skip(startIndex + 1));
}