How to remove lines from markers in the legend

I’ve plotted some data as error bars linked by lines, as you can see from the
picture.

I would like to show only the markers in the legend (I don't want to show the lines in the middle of the markers). I don't want to remove the lines from the diagram, only in the legend.

I tried the code below from this thread:

handles, labels = ax.get_legend_handles_labels()
for h in handles: h.set_linestyle("")
ax.legend(handles, labels)

It removed the lines also from the diagram.

Is there a way to do it?

Updating...
There is a specific option to do this...

import numpy as np
import matplotlib.pyplot as plt

# dummy data
x = np.arange(10)
y1 = 2*x
y2 = 3*x

fig, ax = plt.subplots()

line1, = ax.plot(x, y1, c='blue', marker='x')
line2, = ax.plot(x, y2, c='red', marker='o')

ax.legend([line1, line2], ['data1', 'data2'], handlelength=0.)
plt.show()

Instead of drawing the graph twice, which might come with some overhead, you could use matplotlib.rcParams['legend.handlelength'] = 0. This is a global parameter, which means it would affect every other graph after the fact.

import matplotlib.pyplot as plt
import matplotlib
import numpy as np

matplotlib.rcParams['legend.handlelength'] = 0


x = np.linspace(-np.pi/2, np.pi/2, 31)
y = np.cos(x)**3

# 1) remove points where y > 0.7
x2 = x[y <= 0.7]
y2 = y[y <= 0.7]

# 2) mask points where y > 0.7
y3 = np.ma.masked_where(y > 0.7, y)

# 3) set to NaN where y > 0.7
y4 = y.copy()
y4[y3 > 0.7] = np.nan

plt.plot(x*0.1, y, 'o-', color='lightgrey', label='No mask')
plt.plot(x2*0.4, y2, 'o-', label='Points removed')
plt.plot(x*0.7, y3, 'o-', label='Masked values')
plt.plot(x*1.0, y4, 'o-', label='NaN values')
plt.legend()
plt.title('Masked and NaN data')
plt.show()

If you want to only use it for one graph, you can wrap the code responsible for the graph with:

with plt.rc_context({"legend.handlelength": 0,}):

EDIT: the other answer has a better solution for per graph legends.